﻿/*******************************************************************************
*                                                                              *
* Author    :  Angus Johnson                                                   *
* Version   :  6.4.2                                                           *
* Date      :  27 February 2017                                                *
* Website   :  http://www.angusj.com                                           *
* Copyright :  Angus Johnson 2010-2017                                         *
*                                                                              *
* License:                                                                     *
* Use, modification & distribution is subject to Boost Software License Ver 1. *
* http://www.boost.org/LICENSE_1_0.txt                                         *
*                                                                              *
* Attributions:                                                                *
* The code in this library is an extension of Bala Vatti's clipping algorithm: *
* "A generic solution to polygon clipping"                                     *
* Communications of the ACM, Vol 35, Issue 7 (July 1992) pp 56-63.             *
* http://portal.acm.org/citation.cfm?id=129906                                 *
*                                                                              *
* Computer graphics and geometric modeling: implementation and algorithms      *
* By Max K. Agoston                                                            *
* Springer; 1 edition (January 4, 2005)                                        *
* http://books.google.com/books?q=vatti+clipping+agoston                       *
*                                                                              *
* See also:                                                                    *
* "Polygon Offsetting by Computing Winding Numbers"                            *
* Paper no. DETC2005-85513 pp. 565-575                                         *
* ASME 2005 International Design Engineering Technical Conferences             *
* and Computers and Information in Engineering Conference (IDETC/CIE2005)      *
* September 24-28, 2005 , Long Beach, California, USA                          *
* http://www.me.berkeley.edu/~mcmains/pubs/DAC05OffsetPolygon.pdf              *
*                                                                              *
*******************************************************************************/

/*******************************************************************************
*                                                                              *
* This is a translation of the Delphi Clipper library and the naming style     *
* used has retained a Delphi flavour.                                          *
*                                                                              *
*******************************************************************************/

//use_int32: When enabled 32bit ints are used instead of 64bit ints. This
//improve performance but coordinate values are limited to the range +/- 46340
//#define use_int32

//use_xyz: adds a Z member to IntPoint. Adds a minor cost to performance.
//#define use_xyz

//use_lines: Enables open path clipping. Adds a very minor cost to performance.
#define use_lines


using System;
using System.Collections.Generic;
using System.Threading.Tasks;
//using System.Text;          //for Int128.AsString() & StringBuilder
//using System.IO;            //debugging with streamReader & StreamWriter
//using System.Windows.Forms; //debugging to clipboard

namespace ClipperLib
{

#if use_int32
  using cInt = Int32;
#else
	using cInt = Int64;
#endif

	using Path = List<IntPoint>;
	using Paths = List<List<IntPoint>>;

	public struct DoublePoint
	{
		public double X;
		public double Y;

		public DoublePoint(double x = 0, double y = 0)
		{
			this.X = x; this.Y = y;
		}
		public DoublePoint(DoublePoint dp)
		{
			this.X = dp.X; this.Y = dp.Y;
		}
		public DoublePoint(IntPoint ip)
		{
			this.X = ip.X; this.Y = ip.Y;
		}
	};


	//------------------------------------------------------------------------------
	// PolyTree & PolyNode classes
	//------------------------------------------------------------------------------

	public class PolyTree : PolyNode
	{
		internal List<PolyNode> m_AllPolys = new List<PolyNode>();

		//The GC probably handles this cleanup more efficiently ...
		//~PolyTree(){Clear();}

		public void Clear()
		{
			for (int i = 0; i < m_AllPolys.Count; i++)
				m_AllPolys[i] = null;
			m_AllPolys.Clear();
			m_Childs.Clear();
		}

		public PolyNode GetFirst()
		{
			if (m_Childs.Count > 0)
				return m_Childs[0];
			else
				return null;
		}

		public int Total
		{
			get
			{
				int result = m_AllPolys.Count;
				//with negative offsets, ignore the hidden outer polygon ...
				if (result > 0 && m_Childs[0] != m_AllPolys[0]) result--;
				return result;
			}
		}

	}

	public class PolyNode
	{
		internal PolyNode m_Parent;
		internal Path m_polygon = new Path();
		internal int m_Index;
		internal JoinType m_jointype;
		internal EndType m_endtype;
		internal List<PolyNode> m_Childs = new List<PolyNode>();

		private bool IsHoleNode()
		{
			bool result = true;
			PolyNode node = m_Parent;
			while (node != null)
			{
				result = !result;
				node = node.m_Parent;
			}
			return result;
		}

		public int ChildCount
		{
			get { return m_Childs.Count; }
		}

		public Path Contour
		{
			get { return m_polygon; }
		}

		internal void AddChild(PolyNode Child)
		{
			int cnt = m_Childs.Count;
			m_Childs.Add(Child);
			Child.m_Parent = this;
			Child.m_Index = cnt;
		}

		public PolyNode GetNext()
		{
			if (m_Childs.Count > 0)
				return m_Childs[0];
			else
				return GetNextSiblingUp();
		}

		internal PolyNode GetNextSiblingUp()
		{
			if (m_Parent == null)
				return null;
			else if (m_Index == m_Parent.m_Childs.Count - 1)
				return m_Parent.GetNextSiblingUp();
			else
				return m_Parent.m_Childs[m_Index + 1];
		}

		public List<PolyNode> Childs
		{
			get { return m_Childs; }
		}

		public PolyNode Parent
		{
			get { return m_Parent; }
		}

		public bool IsHole
		{
			get { return IsHoleNode(); }
		}

		public bool IsOpen { get; set; }
	}


	//------------------------------------------------------------------------------
	// Int128 struct (enables safe math on signed 64bit integers)
	// eg Int128 val1((Int64)9223372036854775807); //ie 2^63 -1
	//    Int128 val2((Int64)9223372036854775807);
	//    Int128 val3 = val1 * val2;
	//    val3.ToString => "85070591730234615847396907784232501249" (8.5e+37)
	//------------------------------------------------------------------------------

	internal struct Int128
	{
		private Int64 hi;
		private UInt64 lo;

		public Int128(Int64 _lo)
		{
			lo = (UInt64)_lo;
			if (_lo < 0) hi = -1;
			else hi = 0;
		}

		public Int128(Int64 _hi, UInt64 _lo)
		{
			lo = _lo;
			hi = _hi;
		}

		public Int128(Int128 val)
		{
			hi = val.hi;
			lo = val.lo;
		}

		public bool IsNegative()
		{
			return hi < 0;
		}

		public static bool operator ==(Int128 val1, Int128 val2)
		{
			if ((object)val1 == (object)val2) return true;
			else if ((object)val1 == null || (object)val2 == null) return false;
			return (val1.hi == val2.hi && val1.lo == val2.lo);
		}

		public static bool operator !=(Int128 val1, Int128 val2)
		{
			return !(val1 == val2);
		}

		public override bool Equals(System.Object obj)
		{
			if (obj == null || !(obj is Int128))
				return false;
			Int128 i128 = (Int128)obj;
			return (i128.hi == hi && i128.lo == lo);
		}

		public override int GetHashCode()
		{
			return hi.GetHashCode() ^ lo.GetHashCode();
		}

		public static bool operator >(Int128 val1, Int128 val2)
		{
			if (val1.hi != val2.hi)
				return val1.hi > val2.hi;
			else
				return val1.lo > val2.lo;
		}

		public static bool operator <(Int128 val1, Int128 val2)
		{
			if (val1.hi != val2.hi)
				return val1.hi < val2.hi;
			else
				return val1.lo < val2.lo;
		}

		public static Int128 operator +(Int128 lhs, Int128 rhs)
		{
			lhs.hi += rhs.hi;
			lhs.lo += rhs.lo;
			if (lhs.lo < rhs.lo) lhs.hi++;
			return lhs;
		}

		public static Int128 operator -(Int128 lhs, Int128 rhs)
		{
			return lhs + -rhs;
		}

		public static Int128 operator -(Int128 val)
		{
			if (val.lo == 0)
				return new Int128(-val.hi, 0);
			else
				return new Int128(~val.hi, ~val.lo + 1);
		}

		public static explicit operator double(Int128 val)
		{
			const double shift64 = 18446744073709551616.0; //2^64
			if (val.hi < 0)
			{
				if (val.lo == 0)
					return (double)val.hi * shift64;
				else
					return -(double)(~val.lo + ~val.hi * shift64);
			}
			else
				return (double)(val.lo + val.hi * shift64);
		}

		//nb: Constructing two new Int128 objects every time we want to multiply longs  
		//is slow. So, although calling the Int128Mul method doesn't look as clean, the 
		//code runs significantly faster than if we'd used the * operator.

		public static Int128 Int128Mul(Int64 lhs, Int64 rhs)
		{
			bool negate = (lhs < 0) != (rhs < 0);
			if (lhs < 0) lhs = -lhs;
			if (rhs < 0) rhs = -rhs;
			UInt64 int1Hi = (UInt64)lhs >> 32;
			UInt64 int1Lo = (UInt64)lhs & 0xFFFFFFFF;
			UInt64 int2Hi = (UInt64)rhs >> 32;
			UInt64 int2Lo = (UInt64)rhs & 0xFFFFFFFF;

			//nb: see comments in clipper.pas
			UInt64 a = int1Hi * int2Hi;
			UInt64 b = int1Lo * int2Lo;
			UInt64 c = int1Hi * int2Lo + int1Lo * int2Hi;

			UInt64 lo;
			Int64 hi;
			hi = (Int64)(a + (c >> 32));

			unchecked { lo = (c << 32) + b; }
			if (lo < b) hi++;
			Int128 result = new Int128(hi, lo);
			return negate ? -result : result;
		}

	};

	//------------------------------------------------------------------------------
	//------------------------------------------------------------------------------

	public struct IntPoint
	{
		public cInt X;
		public cInt Y;
#if use_xyz
    public cInt Z;
    
    public IntPoint(cInt x, cInt y, cInt z = 0)
    {
      this.X = x; this.Y = y; this.Z = z;
    }
    
    public IntPoint(double x, double y, double z = 0)
    {
      this.X = (cInt)x; this.Y = (cInt)y; this.Z = (cInt)z;
    }
    
    public IntPoint(DoublePoint dp)
    {
      this.X = (cInt)dp.X; this.Y = (cInt)dp.Y; this.Z = 0;
    }

    public IntPoint(IntPoint pt)
    {
      this.X = pt.X; this.Y = pt.Y; this.Z = pt.Z;
    }
#else
		public IntPoint(cInt X, cInt Y)
		{
			this.X = X; this.Y = Y;
		}
		public IntPoint(double x, double y)
		{
			this.X = (cInt)x; this.Y = (cInt)y;
		}

		public IntPoint(IntPoint pt)
		{
			this.X = pt.X; this.Y = pt.Y;
		}
#endif

		public static bool operator ==(IntPoint a, IntPoint b)
		{
			return a.X == b.X && a.Y == b.Y;
		}

		public static bool operator !=(IntPoint a, IntPoint b)
		{
			return a.X != b.X || a.Y != b.Y;
		}

		public override bool Equals(object obj)
		{
			if (obj == null) return false;
			if (obj is IntPoint)
			{
				IntPoint a = (IntPoint)obj;
				return (X == a.X) && (Y == a.Y);
			}
			else return false;
		}

		public override int GetHashCode()
		{
			//simply prevents a compiler warning
			return base.GetHashCode();
		}

	}// end struct IntPoint

	public struct IntRect
	{
		public cInt left;
		public cInt top;
		public cInt right;
		public cInt bottom;

		public IntRect(cInt l, cInt t, cInt r, cInt b)
		{
			this.left = l; this.top = t;
			this.right = r; this.bottom = b;
		}
		public IntRect(IntRect ir)
		{
			this.left = ir.left; this.top = ir.top;
			this.right = ir.right; this.bottom = ir.bottom;
		}
	}

	public enum ClipType { ctIntersection, ctUnion, ctDifference, ctXor };
	public enum PolyType { ptSubject, ptClip };

	//By far the most widely used winding rules for polygon filling are
	//EvenOdd & NonZero (GDI, GDI+, XLib, OpenGL, Cairo, AGG, Quartz, SVG, Gr32)
	//Others rules include Positive, Negative and ABS_GTR_EQ_TWO (only in OpenGL)
	//see http://glprogramming.com/red/chapter11.html
	public enum PolyFillType { pftEvenOdd, pftNonZero, pftPositive, pftNegative };

	public enum JoinType { jtSquare, jtRound, jtMiter };
	public enum EndType { etClosedPolygon, etClosedLine, etOpenButt, etOpenSquare, etOpenRound };

	internal enum EdgeSide { esLeft, esRight };
	internal enum Direction { dRightToLeft, dLeftToRight };

	internal class TEdge
	{
		internal IntPoint Bot;
		internal IntPoint Curr; //current (updated for every new scanbeam)
		internal IntPoint Top;
		internal IntPoint Delta;
		internal double Dx;
		internal PolyType PolyTyp;
		internal EdgeSide Side; //side only refers to current side of solution poly
		internal int WindDelta; //1 or -1 depending on winding direction
		internal int WindCnt;
		internal int WindCnt2; //winding count of the opposite polytype
		internal int OutIdx;
		internal TEdge Next;
		internal TEdge Prev;
		internal TEdge NextInLML;
		internal TEdge NextInAEL;
		internal TEdge PrevInAEL;
		internal TEdge NextInSEL;
		internal TEdge PrevInSEL;
	};

	public class IntersectNode
	{
		internal TEdge Edge1;
		internal TEdge Edge2;
		internal IntPoint Pt;
	};

	public class MyIntersectNodeSort : IComparer<IntersectNode>
	{
		public int Compare(IntersectNode node1, IntersectNode node2)
		{
			cInt i = node2.Pt.Y - node1.Pt.Y;
			if (i > 0) return 1;
			else if (i < 0) return -1;
			else return 0;
		}
	}

	internal class LocalMinima
	{
		internal cInt Y;
		internal TEdge LeftBound;
		internal TEdge RightBound;
		internal LocalMinima Next;
	};

	internal class Scanbeam
	{
		internal cInt Y;
		internal Scanbeam Next;
	};

	internal class Maxima
	{
		internal cInt X;
		internal Maxima Next;
		internal Maxima Prev;
	};

	//OutRec: contains a path in the clipping solution. Edges in the AEL will
	//carry a pointer to an OutRec when they are part of the clipping solution.
	internal class OutRec
	{
		internal int Idx;
		internal bool IsHole;
		internal bool IsOpen;
		internal OutRec FirstLeft; //see comments in clipper.pas
		internal OutPt Pts;
		internal OutPt BottomPt;
		internal PolyNode PolyNode;
	};

	internal class OutPt
	{
		internal int Idx;
		internal IntPoint Pt;
		internal OutPt Next;
		internal OutPt Prev;
	};

	internal class Join
	{
		internal OutPt OutPt1;
		internal OutPt OutPt2;
		internal IntPoint OffPt;
	};

	public class ClipperBase
	{
		internal const double horizontal = -3.4E+38;
		internal const int Skip = -2;
		internal const int Unassigned = -1;
		internal const double tolerance = 1.0E-20;
		internal static bool near_zero(double val) { return (val > -tolerance) && (val < tolerance); }

#if use_int32
    public const cInt loRange = 0x7FFF;
    public const cInt hiRange = 0x7FFF;
#else
		public const cInt loRange = 0x3FFFFFFF;
		public const cInt hiRange = 0x3FFFFFFFFFFFFFFFL;
#endif

		internal LocalMinima m_MinimaList;
		internal LocalMinima m_CurrentLM;
		internal List<List<TEdge>> m_edges = new List<List<TEdge>>();
		internal Scanbeam m_Scanbeam;
		internal List<OutRec> m_PolyOuts;
		internal TEdge m_ActiveEdges;
		internal bool m_UseFullRange;
		internal bool m_HasOpenPaths;

		//------------------------------------------------------------------------------

		public bool PreserveCollinear
		{
			get;
			set;
		}
		//------------------------------------------------------------------------------

		public void Swap(ref cInt val1, ref cInt val2)
		{
			cInt tmp = val1;
			val1 = val2;
			val2 = tmp;
		}
		//------------------------------------------------------------------------------

		internal static bool IsHorizontal(TEdge e)
		{
			return e.Delta.Y == 0;
		}
		//------------------------------------------------------------------------------

		internal bool PointIsVertex(IntPoint pt, OutPt pp)
		{
			OutPt pp2 = pp;
			do
			{
				if (pp2.Pt == pt) return true;
				pp2 = pp2.Next;
			}
			while (pp2 != pp);
			return false;
		}
		//------------------------------------------------------------------------------

		internal bool PointOnLineSegment(IntPoint pt,
			IntPoint linePt1, IntPoint linePt2, bool UseFullRange)
		{
			if (UseFullRange)
				return ((pt.X == linePt1.X) && (pt.Y == linePt1.Y)) ||
				  ((pt.X == linePt2.X) && (pt.Y == linePt2.Y)) ||
				  (((pt.X > linePt1.X) == (pt.X < linePt2.X)) &&
				  ((pt.Y > linePt1.Y) == (pt.Y < linePt2.Y)) &&
				  ((Int128.Int128Mul((pt.X - linePt1.X), (linePt2.Y - linePt1.Y)) ==
				  Int128.Int128Mul((linePt2.X - linePt1.X), (pt.Y - linePt1.Y)))));
			else
				return ((pt.X == linePt1.X) && (pt.Y == linePt1.Y)) ||
				  ((pt.X == linePt2.X) && (pt.Y == linePt2.Y)) ||
				  (((pt.X > linePt1.X) == (pt.X < linePt2.X)) &&
				  ((pt.Y > linePt1.Y) == (pt.Y < linePt2.Y)) &&
				  ((pt.X - linePt1.X) * (linePt2.Y - linePt1.Y) ==
					(linePt2.X - linePt1.X) * (pt.Y - linePt1.Y)));
		}
		//------------------------------------------------------------------------------

		internal bool PointOnPolygon(IntPoint pt, OutPt pp, bool UseFullRange)
		{
			OutPt pp2 = pp;
			while (true)
			{
				if (PointOnLineSegment(pt, pp2.Pt, pp2.Next.Pt, UseFullRange))
					return true;
				pp2 = pp2.Next;
				if (pp2 == pp) break;
			}
			return false;
		}
		//------------------------------------------------------------------------------

		internal static bool SlopesEqual(TEdge e1, TEdge e2, bool UseFullRange)
		{
			if (UseFullRange)
				return Int128.Int128Mul(e1.Delta.Y, e2.Delta.X) ==
					Int128.Int128Mul(e1.Delta.X, e2.Delta.Y);
			else return (cInt)(e1.Delta.Y) * (e2.Delta.X) ==
			  (cInt)(e1.Delta.X) * (e2.Delta.Y);
		}
		//------------------------------------------------------------------------------

		internal static bool SlopesEqual(IntPoint pt1, IntPoint pt2,
			IntPoint pt3, bool UseFullRange)
		{
			if (UseFullRange)
				return Int128.Int128Mul(pt1.Y - pt2.Y, pt2.X - pt3.X) ==
				  Int128.Int128Mul(pt1.X - pt2.X, pt2.Y - pt3.Y);
			else return
			  (cInt)(pt1.Y - pt2.Y) * (pt2.X - pt3.X) - (cInt)(pt1.X - pt2.X) * (pt2.Y - pt3.Y) == 0;
		}
		//------------------------------------------------------------------------------

		internal static bool SlopesEqual(IntPoint pt1, IntPoint pt2,
			IntPoint pt3, IntPoint pt4, bool UseFullRange)
		{
			if (UseFullRange)
				return Int128.Int128Mul(pt1.Y - pt2.Y, pt3.X - pt4.X) ==
				  Int128.Int128Mul(pt1.X - pt2.X, pt3.Y - pt4.Y);
			else return
			  (cInt)(pt1.Y - pt2.Y) * (pt3.X - pt4.X) - (cInt)(pt1.X - pt2.X) * (pt3.Y - pt4.Y) == 0;
		}
		//------------------------------------------------------------------------------

		internal ClipperBase() //constructor (nb: no external instantiation)
		{
			m_MinimaList = null;
			m_CurrentLM = null;
			m_UseFullRange = false;
			m_HasOpenPaths = false;
		}
		//------------------------------------------------------------------------------

		public virtual void Clear()
		{
			DisposeLocalMinimaList();
			for (int i = 0; i < m_edges.Count; ++i)
			{
				for (int j = 0; j < m_edges[i].Count; ++j) m_edges[i][j] = null;
				m_edges[i].Clear();
			}
			m_edges.Clear();
			m_UseFullRange = false;
			m_HasOpenPaths = false;
		}
		//------------------------------------------------------------------------------

		private void DisposeLocalMinimaList()
		{
			while (m_MinimaList != null)
			{
				LocalMinima tmpLm = m_MinimaList.Next;
				m_MinimaList = null;
				m_MinimaList = tmpLm;
			}
			m_CurrentLM = null;
		}
		//------------------------------------------------------------------------------

		void RangeTest(IntPoint Pt, ref bool useFullRange)
		{
			if (useFullRange)
			{
				if (Pt.X > hiRange || Pt.Y > hiRange || -Pt.X > hiRange || -Pt.Y > hiRange)
					throw new ClipperException("Coordinate outside allowed range");
			}
			else if (Pt.X > loRange || Pt.Y > loRange || -Pt.X > loRange || -Pt.Y > loRange)
			{
				useFullRange = true;
				RangeTest(Pt, ref useFullRange);
			}
		}
		//------------------------------------------------------------------------------

		private void InitEdge(TEdge e, TEdge eNext,
		  TEdge ePrev, IntPoint pt)
		{
			e.Next = eNext;
			e.Prev = ePrev;
			e.Curr = pt;
			e.OutIdx = Unassigned;
		}
		//------------------------------------------------------------------------------

		private void InitEdge2(TEdge e, PolyType polyType)
		{
			if (e.Curr.Y >= e.Next.Curr.Y)
			{
				e.Bot = e.Curr;
				e.Top = e.Next.Curr;
			}
			else
			{
				e.Top = e.Curr;
				e.Bot = e.Next.Curr;
			}
			SetDx(e);
			e.PolyTyp = polyType;
		}
		//------------------------------------------------------------------------------

		private TEdge FindNextLocMin(TEdge E)
		{
			TEdge E2;
			for (; ; )
			{
				while (E.Bot != E.Prev.Bot || E.Curr == E.Top) E = E.Next;
				if (E.Dx != horizontal && E.Prev.Dx != horizontal) break;
				while (E.Prev.Dx == horizontal) E = E.Prev;
				E2 = E;
				while (E.Dx == horizontal) E = E.Next;
				if (E.Top.Y == E.Prev.Bot.Y) continue; //ie just an intermediate horz.
				if (E2.Prev.Bot.X < E.Bot.X) E = E2;
				break;
			}
			return E;
		}
		//------------------------------------------------------------------------------

		private TEdge ProcessBound(TEdge E, bool LeftBoundIsForward)
		{
			TEdge EStart, Result = E;
			TEdge Horz;

			if (Result.OutIdx == Skip)
			{
				//check if there are edges beyond the skip edge in the bound and if so
				//create another LocMin and calling ProcessBound once more ...
				E = Result;
				if (LeftBoundIsForward)
				{
					while (E.Top.Y == E.Next.Bot.Y) E = E.Next;
					while (E != Result && E.Dx == horizontal) E = E.Prev;
				}
				else
				{
					while (E.Top.Y == E.Prev.Bot.Y) E = E.Prev;
					while (E != Result && E.Dx == horizontal) E = E.Next;
				}
				if (E == Result)
				{
					if (LeftBoundIsForward) Result = E.Next;
					else Result = E.Prev;
				}
				else
				{
					//there are more edges in the bound beyond result starting with E
					if (LeftBoundIsForward)
						E = Result.Next;
					else
						E = Result.Prev;
					LocalMinima locMin = new LocalMinima();
					locMin.Next = null;
					locMin.Y = E.Bot.Y;
					locMin.LeftBound = null;
					locMin.RightBound = E;
					E.WindDelta = 0;
					Result = ProcessBound(E, LeftBoundIsForward);
					InsertLocalMinima(locMin);
				}
				return Result;
			}

			if (E.Dx == horizontal)
			{
				//We need to be careful with open paths because this may not be a
				//true local minima (ie E may be following a skip edge).
				//Also, consecutive horz. edges may start heading left before going right.
				if (LeftBoundIsForward) EStart = E.Prev;
				else EStart = E.Next;
				if (EStart.Dx == horizontal) //ie an adjoining horizontal skip edge
				{
					if (EStart.Bot.X != E.Bot.X && EStart.Top.X != E.Bot.X)
						ReverseHorizontal(E);
				}
				else if (EStart.Bot.X != E.Bot.X)
					ReverseHorizontal(E);
			}

			EStart = E;
			if (LeftBoundIsForward)
			{
				while (Result.Top.Y == Result.Next.Bot.Y && Result.Next.OutIdx != Skip)
					Result = Result.Next;
				if (Result.Dx == horizontal && Result.Next.OutIdx != Skip)
				{
					//nb: at the top of a bound, horizontals are added to the bound
					//only when the preceding edge attaches to the horizontal's left vertex
					//unless a Skip edge is encountered when that becomes the top divide
					Horz = Result;
					while (Horz.Prev.Dx == horizontal) Horz = Horz.Prev;
					if (Horz.Prev.Top.X > Result.Next.Top.X) Result = Horz.Prev;
				}
				while (E != Result)
				{
					E.NextInLML = E.Next;
					if (E.Dx == horizontal && E != EStart && E.Bot.X != E.Prev.Top.X)
						ReverseHorizontal(E);
					E = E.Next;
				}
				if (E.Dx == horizontal && E != EStart && E.Bot.X != E.Prev.Top.X)
					ReverseHorizontal(E);
				Result = Result.Next; //move to the edge just beyond current bound
			}
			else
			{
				while (Result.Top.Y == Result.Prev.Bot.Y && Result.Prev.OutIdx != Skip)
					Result = Result.Prev;
				if (Result.Dx == horizontal && Result.Prev.OutIdx != Skip)
				{
					Horz = Result;
					while (Horz.Next.Dx == horizontal) Horz = Horz.Next;
					if (Horz.Next.Top.X == Result.Prev.Top.X ||
						Horz.Next.Top.X > Result.Prev.Top.X) Result = Horz.Next;
				}

				while (E != Result)
				{
					E.NextInLML = E.Prev;
					if (E.Dx == horizontal && E != EStart && E.Bot.X != E.Next.Top.X)
						ReverseHorizontal(E);
					E = E.Prev;
				}
				if (E.Dx == horizontal && E != EStart && E.Bot.X != E.Next.Top.X)
					ReverseHorizontal(E);
				Result = Result.Prev; //move to the edge just beyond current bound
			}
			return Result;
		}
		//------------------------------------------------------------------------------


		public bool AddPath(Path pg, PolyType polyType, bool Closed)
		{
#if use_lines
			if (!Closed && polyType == PolyType.ptClip)
				throw new ClipperException("AddPath: Open paths must be subject.");
#else
      if (!Closed)
        throw new ClipperException("AddPath: Open paths have been disabled.");
#endif

			int highI = (int)pg.Count - 1;
			if (Closed) while (highI > 0 && (pg[highI] == pg[0])) --highI;
			while (highI > 0 && (pg[highI] == pg[highI - 1])) --highI;
			if ((Closed && highI < 2) || (!Closed && highI < 1)) return false;

			//create a new edge array ...
			List<TEdge> edges = new List<TEdge>(highI + 1);
			for (int i = 0; i <= highI; i++) edges.Add(new TEdge());

			bool IsFlat = true;

			//1. Basic (first) edge initialization ...
			edges[1].Curr = pg[1];
			RangeTest(pg[0], ref m_UseFullRange);
			RangeTest(pg[highI], ref m_UseFullRange);
			InitEdge(edges[0], edges[1], edges[highI], pg[0]);
			InitEdge(edges[highI], edges[0], edges[highI - 1], pg[highI]);
			for (int i = highI - 1; i >= 1; --i)
			{
				RangeTest(pg[i], ref m_UseFullRange);
				InitEdge(edges[i], edges[i + 1], edges[i - 1], pg[i]);
			}
			TEdge eStart = edges[0];

			//2. Remove duplicate vertices, and (when closed) collinear edges ...
			TEdge E = eStart, eLoopStop = eStart;
			for (; ; )
			{
				//nb: allows matching start and end points when not Closed ...
				if (E.Curr == E.Next.Curr && (Closed || E.Next != eStart))
				{
					if (E == E.Next) break;
					if (E == eStart) eStart = E.Next;
					E = RemoveEdge(E);
					eLoopStop = E;
					continue;
				}
				if (E.Prev == E.Next)
					break; //only two vertices
				else if (Closed &&
				  SlopesEqual(E.Prev.Curr, E.Curr, E.Next.Curr, m_UseFullRange) &&
				  (!PreserveCollinear ||
				  !Pt2IsBetweenPt1AndPt3(E.Prev.Curr, E.Curr, E.Next.Curr)))
				{
					//Collinear edges are allowed for open paths but in closed paths
					//the default is to merge adjacent collinear edges into a single edge.
					//However, if the PreserveCollinear property is enabled, only overlapping
					//collinear edges (ie spikes) will be removed from closed paths.
					if (E == eStart) eStart = E.Next;
					E = RemoveEdge(E);
					E = E.Prev;
					eLoopStop = E;
					continue;
				}
				E = E.Next;
				if ((E == eLoopStop) || (!Closed && E.Next == eStart)) break;
			}

			if ((!Closed && (E == E.Next)) || (Closed && (E.Prev == E.Next)))
				return false;

			if (!Closed)
			{
				m_HasOpenPaths = true;
				eStart.Prev.OutIdx = Skip;
			}

			//3. Do second stage of edge initialization ...
			E = eStart;
			do
			{
				InitEdge2(E, polyType);
				E = E.Next;
				if (IsFlat && E.Curr.Y != eStart.Curr.Y) IsFlat = false;
			}
			while (E != eStart);

			//4. Finally, add edge bounds to LocalMinima list ...

			//Totally flat paths must be handled differently when adding them
			//to LocalMinima list to avoid endless loops etc ...
			if (IsFlat)
			{
				if (Closed) return false;
				E.Prev.OutIdx = Skip;
				LocalMinima locMin = new LocalMinima();
				locMin.Next = null;
				locMin.Y = E.Bot.Y;
				locMin.LeftBound = null;
				locMin.RightBound = E;
				locMin.RightBound.Side = EdgeSide.esRight;
				locMin.RightBound.WindDelta = 0;
				for (; ; )
				{
					if (E.Bot.X != E.Prev.Top.X) ReverseHorizontal(E);
					if (E.Next.OutIdx == Skip) break;
					E.NextInLML = E.Next;
					E = E.Next;
				}
				InsertLocalMinima(locMin);
				m_edges.Add(edges);
				return true;
			}

			m_edges.Add(edges);
			bool leftBoundIsForward;
			TEdge EMin = null;

			//workaround to avoid an endless loop in the while loop below when
			//open paths have matching start and end points ...
			if (E.Prev.Bot == E.Prev.Top) E = E.Next;

			for (; ; )
			{
				E = FindNextLocMin(E);
				if (E == EMin) break;
				else if (EMin == null) EMin = E;

				//E and E.Prev now share a local minima (left aligned if horizontal).
				//Compare their slopes to find which starts which bound ...
				LocalMinima locMin = new LocalMinima();
				locMin.Next = null;
				locMin.Y = E.Bot.Y;
				if (E.Dx < E.Prev.Dx)
				{
					locMin.LeftBound = E.Prev;
					locMin.RightBound = E;
					leftBoundIsForward = false; //Q.nextInLML = Q.prev
				}
				else
				{
					locMin.LeftBound = E;
					locMin.RightBound = E.Prev;
					leftBoundIsForward = true; //Q.nextInLML = Q.next
				}
				locMin.LeftBound.Side = EdgeSide.esLeft;
				locMin.RightBound.Side = EdgeSide.esRight;

				if (!Closed) locMin.LeftBound.WindDelta = 0;
				else if (locMin.LeftBound.Next == locMin.RightBound)
					locMin.LeftBound.WindDelta = -1;
				else locMin.LeftBound.WindDelta = 1;
				locMin.RightBound.WindDelta = -locMin.LeftBound.WindDelta;

				E = ProcessBound(locMin.LeftBound, leftBoundIsForward);
				if (E.OutIdx == Skip) E = ProcessBound(E, leftBoundIsForward);

				TEdge E2 = ProcessBound(locMin.RightBound, !leftBoundIsForward);
				if (E2.OutIdx == Skip) E2 = ProcessBound(E2, !leftBoundIsForward);

				if (locMin.LeftBound.OutIdx == Skip)
					locMin.LeftBound = null;
				else if (locMin.RightBound.OutIdx == Skip)
					locMin.RightBound = null;
				InsertLocalMinima(locMin);
				if (!leftBoundIsForward) E = E2;
			}
			return true;

		}
		//------------------------------------------------------------------------------

		public bool AddPaths(Paths ppg, PolyType polyType, bool closed)
		{
			bool result = false;

			for (int i = 0; i < ppg.Count; ++i)
				if (AddPath(ppg[i], polyType, closed)) result = true;


			return result;
		}
		//------------------------------------------------------------------------------

		internal bool Pt2IsBetweenPt1AndPt3(IntPoint pt1, IntPoint pt2, IntPoint pt3)
		{
			if ((pt1 == pt3) || (pt1 == pt2) || (pt3 == pt2)) return false;
			else if (pt1.X != pt3.X) return (pt2.X > pt1.X) == (pt2.X < pt3.X);
			else return (pt2.Y > pt1.Y) == (pt2.Y < pt3.Y);
		}
		//------------------------------------------------------------------------------

		TEdge RemoveEdge(TEdge e)
		{
			//removes e from double_linked_list (but without removing from memory)
			e.Prev.Next = e.Next;
			e.Next.Prev = e.Prev;
			TEdge result = e.Next;
			e.Prev = null; //flag as removed (see ClipperBase.Clear)
			return result;
		}
		//------------------------------------------------------------------------------

		private void SetDx(TEdge e)
		{
			e.Delta.X = (e.Top.X - e.Bot.X);
			e.Delta.Y = (e.Top.Y - e.Bot.Y);
			if (e.Delta.Y == 0) e.Dx = horizontal;
			else e.Dx = (double)(e.Delta.X) / (e.Delta.Y);
		}
		//---------------------------------------------------------------------------

		private void InsertLocalMinima(LocalMinima newLm)
		{
			if (m_MinimaList == null)
			{
				m_MinimaList = newLm;
			}
			else if (newLm.Y >= m_MinimaList.Y)
			{
				newLm.Next = m_MinimaList;
				m_MinimaList = newLm;
			}
			else
			{
				LocalMinima tmpLm = m_MinimaList;
				while (tmpLm.Next != null && (newLm.Y < tmpLm.Next.Y))
					tmpLm = tmpLm.Next;
				newLm.Next = tmpLm.Next;
				tmpLm.Next = newLm;
			}
		}
		//------------------------------------------------------------------------------

		internal Boolean PopLocalMinima(cInt Y, out LocalMinima current)
		{
			current = m_CurrentLM;
			if (m_CurrentLM != null && m_CurrentLM.Y == Y)
			{
				m_CurrentLM = m_CurrentLM.Next;
				return true;
			}
			return false;
		}
		//------------------------------------------------------------------------------

		private void ReverseHorizontal(TEdge e)
		{
			//swap horizontal edges' top and bottom x's so they follow the natural
			//progression of the bounds - ie so their xbots will align with the
			//adjoining lower edge. [Helpful in the ProcessHorizontal() method.]
			Swap(ref e.Top.X, ref e.Bot.X);
#if use_xyz
      Swap(ref e.Top.Z, ref e.Bot.Z);
#endif
		}
		//------------------------------------------------------------------------------

		internal virtual void Reset()
		{
			m_CurrentLM = m_MinimaList;
			if (m_CurrentLM == null) return; //ie nothing to process

			//reset all edges ...
			m_Scanbeam = null;
			LocalMinima lm = m_MinimaList;
			while (lm != null)
			{
				InsertScanbeam(lm.Y);
				TEdge e = lm.LeftBound;
				if (e != null)
				{
					e.Curr = e.Bot;
					e.OutIdx = Unassigned;
				}
				e = lm.RightBound;
				if (e != null)
				{
					e.Curr = e.Bot;
					e.OutIdx = Unassigned;
				}
				lm = lm.Next;
			}
			m_ActiveEdges = null;
		}
		//------------------------------------------------------------------------------

		public static IntRect GetBounds(Paths paths)
		{
			int i = 0, cnt = paths.Count;
			while (i < cnt && paths[i].Count == 0) i++;
			if (i == cnt) return new IntRect(0, 0, 0, 0);
			IntRect result = new IntRect();
			result.left = paths[i][0].X;
			result.right = result.left;
			result.top = paths[i][0].Y;
			result.bottom = result.top;
			for (; i < cnt; i++)
				for (int j = 0; j < paths[i].Count; j++)
				{
					if (paths[i][j].X < result.left) result.left = paths[i][j].X;
					else if (paths[i][j].X > result.right) result.right = paths[i][j].X;
					if (paths[i][j].Y < result.top) result.top = paths[i][j].Y;
					else if (paths[i][j].Y > result.bottom) result.bottom = paths[i][j].Y;
				}
			return result;
		}
		//------------------------------------------------------------------------------

		internal void InsertScanbeam(cInt Y)
		{
			//single-linked list: sorted descending, ignoring dups.
			if (m_Scanbeam == null)
			{
				m_Scanbeam = new Scanbeam();
				m_Scanbeam.Next = null;
				m_Scanbeam.Y = Y;
			}
			else if (Y > m_Scanbeam.Y)
			{
				Scanbeam newSb = new Scanbeam();
				newSb.Y = Y;
				newSb.Next = m_Scanbeam;
				m_Scanbeam = newSb;
			}
			else
			{
				Scanbeam sb2 = m_Scanbeam;
				while (sb2.Next != null && (Y <= sb2.Next.Y)) sb2 = sb2.Next;
				if (Y == sb2.Y) return; //ie ignores duplicates
				Scanbeam newSb = new Scanbeam();
				newSb.Y = Y;
				newSb.Next = sb2.Next;
				sb2.Next = newSb;
			}
		}
		//------------------------------------------------------------------------------

		internal Boolean PopScanbeam(out cInt Y)
		{
			if (m_Scanbeam == null)
			{
				Y = 0;
				return false;
			}
			Y = m_Scanbeam.Y;
			m_Scanbeam = m_Scanbeam.Next;
			return true;
		}
		//------------------------------------------------------------------------------

		internal Boolean LocalMinimaPending()
		{
			return (m_CurrentLM != null);
		}
		//------------------------------------------------------------------------------

		internal OutRec CreateOutRec()
		{
			OutRec result = new OutRec();
			result.Idx = Unassigned;
			result.IsHole = false;
			result.IsOpen = false;
			result.FirstLeft = null;
			result.Pts = null;
			result.BottomPt = null;
			result.PolyNode = null;
			m_PolyOuts.Add(result);
			result.Idx = m_PolyOuts.Count - 1;
			return result;
		}
		//------------------------------------------------------------------------------

		internal void DisposeOutRec(int index)
		{
			OutRec outRec = m_PolyOuts[index];
			outRec.Pts = null;
			outRec = null;
			m_PolyOuts[index] = null;
		}
		//------------------------------------------------------------------------------

		internal void UpdateEdgeIntoAEL(ref TEdge e)
		{
			if (e.NextInLML == null)
				throw new ClipperException("UpdateEdgeIntoAEL: invalid call");
			TEdge AelPrev = e.PrevInAEL;
			TEdge AelNext = e.NextInAEL;
			e.NextInLML.OutIdx = e.OutIdx;
			if (AelPrev != null)
				AelPrev.NextInAEL = e.NextInLML;
			else m_ActiveEdges = e.NextInLML;
			if (AelNext != null)
				AelNext.PrevInAEL = e.NextInLML;
			e.NextInLML.Side = e.Side;
			e.NextInLML.WindDelta = e.WindDelta;
			e.NextInLML.WindCnt = e.WindCnt;
			e.NextInLML.WindCnt2 = e.WindCnt2;
			e = e.NextInLML;
			e.Curr = e.Bot;
			e.PrevInAEL = AelPrev;
			e.NextInAEL = AelNext;
			if (!IsHorizontal(e)) InsertScanbeam(e.Top.Y);
		}
		//------------------------------------------------------------------------------

		internal void SwapPositionsInAEL(TEdge edge1, TEdge edge2)
		{
			//check that one or other edge hasn't already been removed from AEL ...
			if (edge1.NextInAEL == edge1.PrevInAEL ||
			  edge2.NextInAEL == edge2.PrevInAEL) return;

			if (edge1.NextInAEL == edge2)
			{
				TEdge next = edge2.NextInAEL;
				if (next != null)
					next.PrevInAEL = edge1;
				TEdge prev = edge1.PrevInAEL;
				if (prev != null)
					prev.NextInAEL = edge2;
				edge2.PrevInAEL = prev;
				edge2.NextInAEL = edge1;
				edge1.PrevInAEL = edge2;
				edge1.NextInAEL = next;
			}
			else if (edge2.NextInAEL == edge1)
			{
				TEdge next = edge1.NextInAEL;
				if (next != null)
					next.PrevInAEL = edge2;
				TEdge prev = edge2.PrevInAEL;
				if (prev != null)
					prev.NextInAEL = edge1;
				edge1.PrevInAEL = prev;
				edge1.NextInAEL = edge2;
				edge2.PrevInAEL = edge1;
				edge2.NextInAEL = next;
			}
			else
			{
				TEdge next = edge1.NextInAEL;
				TEdge prev = edge1.PrevInAEL;
				edge1.NextInAEL = edge2.NextInAEL;
				if (edge1.NextInAEL != null)
					edge1.NextInAEL.PrevInAEL = edge1;
				edge1.PrevInAEL = edge2.PrevInAEL;
				if (edge1.PrevInAEL != null)
					edge1.PrevInAEL.NextInAEL = edge1;
				edge2.NextInAEL = next;
				if (edge2.NextInAEL != null)
					edge2.NextInAEL.PrevInAEL = edge2;
				edge2.PrevInAEL = prev;
				if (edge2.PrevInAEL != null)
					edge2.PrevInAEL.NextInAEL = edge2;
			}

			if (edge1.PrevInAEL == null)
				m_ActiveEdges = edge1;
			else if (edge2.PrevInAEL == null)
				m_ActiveEdges = edge2;
		}
		//------------------------------------------------------------------------------

		internal void DeleteFromAEL(TEdge e)
		{
			TEdge AelPrev = e.PrevInAEL;
			TEdge AelNext = e.NextInAEL;
			if (AelPrev == null && AelNext == null && (e != m_ActiveEdges))
				return; //already deleted
			if (AelPrev != null)
				AelPrev.NextInAEL = AelNext;
			else m_ActiveEdges = AelNext;
			if (AelNext != null)
				AelNext.PrevInAEL = AelPrev;
			e.NextInAEL = null;
			e.PrevInAEL = null;
		}
		//------------------------------------------------------------------------------

	} //end ClipperBase

	public class Clipper : ClipperBase
	{
		//InitOptions that can be passed to the constructor ...
		public const int ioReverseSolution = 1;
		public const int ioStrictlySimple = 2;
		public const int ioPreserveCollinear = 4;

		private ClipType m_ClipType;
		private Maxima m_Maxima;
		private TEdge m_SortedEdges;
		private List<IntersectNode> m_IntersectList;
		IComparer<IntersectNode> m_IntersectNodeComparer;
		private bool m_ExecuteLocked;
		private PolyFillType m_ClipFillType;
		private PolyFillType m_SubjFillType;
		private List<Join> m_Joins;
		private List<Join> m_GhostJoins;
		private bool m_UsingPolyTree;
#if use_xyz
      public delegate void ZFillCallback(IntPoint bot1, IntPoint top1, 
        IntPoint bot2, IntPoint top2, ref IntPoint pt);
      public ZFillCallback ZFillFunction { get; set; }
#endif
		public Clipper(int InitOptions = 0) : base() //constructor
		{
			m_Scanbeam = null;
			m_Maxima = null;
			m_ActiveEdges = null;
			m_SortedEdges = null;
			m_IntersectList = new List<IntersectNode>();
			m_IntersectNodeComparer = new MyIntersectNodeSort();
			m_ExecuteLocked = false;
			m_UsingPolyTree = false;
			m_PolyOuts = new List<OutRec>();
			m_Joins = new List<Join>();
			m_GhostJoins = new List<Join>();
			ReverseSolution = (ioReverseSolution & InitOptions) != 0;
			StrictlySimple = (ioStrictlySimple & InitOptions) != 0;
			PreserveCollinear = (ioPreserveCollinear & InitOptions) != 0;
#if use_xyz
          ZFillFunction = null;
#endif
		}
		//------------------------------------------------------------------------------

		private void InsertMaxima(cInt X)
		{
			//double-linked list: sorted ascending, ignoring dups.
			Maxima newMax = new Maxima();
			newMax.X = X;
			if (m_Maxima == null)
			{
				m_Maxima = newMax;
				m_Maxima.Next = null;
				m_Maxima.Prev = null;
			}
			else if (X < m_Maxima.X)
			{
				newMax.Next = m_Maxima;
				newMax.Prev = null;
				m_Maxima = newMax;
			}
			else
			{
				Maxima m = m_Maxima;
				while (m.Next != null && (X >= m.Next.X)) m = m.Next;
				if (X == m.X) return; //ie ignores duplicates (& CG to clean up newMax)
									  //insert newMax between m and m.Next ...
				newMax.Next = m.Next;
				newMax.Prev = m;
				if (m.Next != null) m.Next.Prev = newMax;
				m.Next = newMax;
			}
		}
		//------------------------------------------------------------------------------

		public bool ReverseSolution
		{
			get;
			set;
		}
		//------------------------------------------------------------------------------

		public bool StrictlySimple
		{
			get;
			set;
		}
		//------------------------------------------------------------------------------

		public bool Execute(ClipType clipType, Paths solution,
			PolyFillType FillType = PolyFillType.pftEvenOdd)
		{
			return Execute(clipType, solution, FillType, FillType);
		}
		//------------------------------------------------------------------------------

		public bool Execute(ClipType clipType, PolyTree polytree,
			PolyFillType FillType = PolyFillType.pftEvenOdd)
		{
			return Execute(clipType, polytree, FillType, FillType);
		}
		//------------------------------------------------------------------------------

		public bool Execute(ClipType clipType, Paths solution,
			PolyFillType subjFillType, PolyFillType clipFillType)
		{
			if (m_ExecuteLocked) return false;
			if (m_HasOpenPaths) throw
			  new ClipperException("Error: PolyTree struct is needed for open path clipping.");

			m_ExecuteLocked = true;
			solution.Clear();
			m_SubjFillType = subjFillType;
			m_ClipFillType = clipFillType;
			m_ClipType = clipType;
			m_UsingPolyTree = false;
			bool succeeded;
			try
			{
				succeeded = ExecuteInternal();
				//build the return polygons ...
				if (succeeded) BuildResult(solution);
			}
			finally
			{
				DisposeAllPolyPts();
				m_ExecuteLocked = false;
			}
			return succeeded;
		}
		//------------------------------------------------------------------------------

		public bool Execute(ClipType clipType, PolyTree polytree,
			PolyFillType subjFillType, PolyFillType clipFillType)
		{
			if (m_ExecuteLocked) return false;
			m_ExecuteLocked = true;
			m_SubjFillType = subjFillType;
			m_ClipFillType = clipFillType;
			m_ClipType = clipType;
			m_UsingPolyTree = true;
			bool succeeded;
			try
			{
				succeeded = ExecuteInternal();
				//build the return polygons ...
				if (succeeded) BuildResult2(polytree);
			}
			finally
			{
				DisposeAllPolyPts();
				m_ExecuteLocked = false;
			}
			return succeeded;
		}
		//------------------------------------------------------------------------------

		internal void FixHoleLinkage(OutRec outRec)
		{
			//skip if an outermost polygon or
			//already already points to the correct FirstLeft ...
			if (outRec.FirstLeft == null ||
				  (outRec.IsHole != outRec.FirstLeft.IsHole &&
				  outRec.FirstLeft.Pts != null)) return;

			OutRec orfl = outRec.FirstLeft;
			while (orfl != null && ((orfl.IsHole == outRec.IsHole) || orfl.Pts == null))
				orfl = orfl.FirstLeft;
			outRec.FirstLeft = orfl;
		}
		//------------------------------------------------------------------------------

		private bool ExecuteInternal()
		{
			try
			{
				Reset();
				m_SortedEdges = null;
				m_Maxima = null;

				cInt botY, topY;
				if (!PopScanbeam(out botY)) return false;
				InsertLocalMinimaIntoAEL(botY);
				while (PopScanbeam(out topY) || LocalMinimaPending())
				{
					ProcessHorizontals();
					m_GhostJoins.Clear();
					if (!ProcessIntersections(topY)) return false;
					ProcessEdgesAtTopOfScanbeam(topY);
					botY = topY;
					InsertLocalMinimaIntoAEL(botY);
				}

				//fix orientations ...
				foreach (OutRec outRec in m_PolyOuts)
				{
					if (outRec.Pts == null || outRec.IsOpen) continue;
					if ((outRec.IsHole ^ ReverseSolution) == (Area(outRec) > 0))
						ReversePolyPtLinks(outRec.Pts);
				}

				JoinCommonEdges();

				foreach (OutRec outRec in m_PolyOuts)
				{
					if (outRec.Pts == null)
						continue;
					else if (outRec.IsOpen)
						FixupOutPolyline(outRec);
					else
						FixupOutPolygon(outRec);
				}

				if (StrictlySimple) DoSimplePolygons();
				return true;
			}
			//catch { return false; }
			finally
			{
				m_Joins.Clear();
				m_GhostJoins.Clear();
			}
		}
		//------------------------------------------------------------------------------

		private void DisposeAllPolyPts()
		{
			for (int i = 0; i < m_PolyOuts.Count; ++i) DisposeOutRec(i);
			m_PolyOuts.Clear();
		}
		//------------------------------------------------------------------------------

		private void AddJoin(OutPt Op1, OutPt Op2, IntPoint OffPt)
		{
			Join j = new Join();
			j.OutPt1 = Op1;
			j.OutPt2 = Op2;
			j.OffPt = OffPt;
			m_Joins.Add(j);
		}
		//------------------------------------------------------------------------------

		private void AddGhostJoin(OutPt Op, IntPoint OffPt)
		{
			Join j = new Join();
			j.OutPt1 = Op;
			j.OffPt = OffPt;
			m_GhostJoins.Add(j);
		}
		//------------------------------------------------------------------------------

#if use_xyz
      internal void SetZ(ref IntPoint pt, TEdge e1, TEdge e2)
      {
        if (pt.Z != 0 || ZFillFunction == null) return;
        else if (pt == e1.Bot) pt.Z = e1.Bot.Z;
        else if (pt == e1.Top) pt.Z = e1.Top.Z;
        else if (pt == e2.Bot) pt.Z = e2.Bot.Z;
        else if (pt == e2.Top) pt.Z = e2.Top.Z;
        else ZFillFunction(e1.Bot, e1.Top, e2.Bot, e2.Top, ref pt);
      }
      //------------------------------------------------------------------------------
#endif

		private void InsertLocalMinimaIntoAEL(cInt botY)
		{
			LocalMinima lm;
			while (PopLocalMinima(botY, out lm))
			{
				TEdge lb = lm.LeftBound;
				TEdge rb = lm.RightBound;

				OutPt Op1 = null;
				if (lb == null)
				{
					InsertEdgeIntoAEL(rb, null);
					SetWindingCount(rb);
					if (IsContributing(rb))
						Op1 = AddOutPt(rb, rb.Bot);
				}
				else if (rb == null)
				{
					InsertEdgeIntoAEL(lb, null);
					SetWindingCount(lb);
					if (IsContributing(lb))
						Op1 = AddOutPt(lb, lb.Bot);
					InsertScanbeam(lb.Top.Y);
				}
				else
				{
					InsertEdgeIntoAEL(lb, null);
					InsertEdgeIntoAEL(rb, lb);
					SetWindingCount(lb);
					rb.WindCnt = lb.WindCnt;
					rb.WindCnt2 = lb.WindCnt2;
					if (IsContributing(lb))
						Op1 = AddLocalMinPoly(lb, rb, lb.Bot);
					InsertScanbeam(lb.Top.Y);
				}

				if (rb != null)
				{
					if (IsHorizontal(rb))
					{
						if (rb.NextInLML != null)
							InsertScanbeam(rb.NextInLML.Top.Y);
						AddEdgeToSEL(rb);
					}
					else
						InsertScanbeam(rb.Top.Y);
				}

				if (lb == null || rb == null) continue;

				//if output polygons share an Edge with a horizontal rb, they'll need joining later ...
				if (Op1 != null && IsHorizontal(rb) &&
				  m_GhostJoins.Count > 0 && rb.WindDelta != 0)
				{
					for (int i = 0; i < m_GhostJoins.Count; i++)
					{
						//if the horizontal Rb and a 'ghost' horizontal overlap, then convert
						//the 'ghost' join to a real join ready for later ...
						Join j = m_GhostJoins[i];
						if (HorzSegmentsOverlap(j.OutPt1.Pt.X, j.OffPt.X, rb.Bot.X, rb.Top.X))
							AddJoin(j.OutPt1, Op1, j.OffPt);
					}
				}

				if (lb.OutIdx >= 0 && lb.PrevInAEL != null &&
				  lb.PrevInAEL.Curr.X == lb.Bot.X &&
				  lb.PrevInAEL.OutIdx >= 0 &&
				  SlopesEqual(lb.PrevInAEL.Curr, lb.PrevInAEL.Top, lb.Curr, lb.Top, m_UseFullRange) &&
				  lb.WindDelta != 0 && lb.PrevInAEL.WindDelta != 0)
				{
					OutPt Op2 = AddOutPt(lb.PrevInAEL, lb.Bot);
					AddJoin(Op1, Op2, lb.Top);
				}

				if (lb.NextInAEL != rb)
				{

					if (rb.OutIdx >= 0 && rb.PrevInAEL.OutIdx >= 0 &&
					  SlopesEqual(rb.PrevInAEL.Curr, rb.PrevInAEL.Top, rb.Curr, rb.Top, m_UseFullRange) &&
					  rb.WindDelta != 0 && rb.PrevInAEL.WindDelta != 0)
					{
						OutPt Op2 = AddOutPt(rb.PrevInAEL, rb.Bot);
						AddJoin(Op1, Op2, rb.Top);
					}

					TEdge e = lb.NextInAEL;
					if (e != null)
						while (e != rb)
						{
							//nb: For calculating winding counts etc, IntersectEdges() assumes
							//that param1 will be to the right of param2 ABOVE the intersection ...
							IntersectEdges(rb, e, lb.Curr); //order important here
							e = e.NextInAEL;
						}
				}
			}
		}
		//------------------------------------------------------------------------------

		private void InsertEdgeIntoAEL(TEdge edge, TEdge startEdge)
		{
			if (m_ActiveEdges == null)
			{
				edge.PrevInAEL = null;
				edge.NextInAEL = null;
				m_ActiveEdges = edge;
			}
			else if (startEdge == null && E2InsertsBeforeE1(m_ActiveEdges, edge))
			{
				edge.PrevInAEL = null;
				edge.NextInAEL = m_ActiveEdges;
				m_ActiveEdges.PrevInAEL = edge;
				m_ActiveEdges = edge;
			}
			else
			{
				if (startEdge == null) startEdge = m_ActiveEdges;
				while (startEdge.NextInAEL != null &&
				  !E2InsertsBeforeE1(startEdge.NextInAEL, edge))
					startEdge = startEdge.NextInAEL;
				edge.NextInAEL = startEdge.NextInAEL;
				if (startEdge.NextInAEL != null) startEdge.NextInAEL.PrevInAEL = edge;
				edge.PrevInAEL = startEdge;
				startEdge.NextInAEL = edge;
			}
		}
		//----------------------------------------------------------------------

		private bool E2InsertsBeforeE1(TEdge e1, TEdge e2)
		{
			if (e2.Curr.X == e1.Curr.X)
			{
				if (e2.Top.Y > e1.Top.Y)
					return e2.Top.X < TopX(e1, e2.Top.Y);
				else return e1.Top.X > TopX(e2, e1.Top.Y);
			}
			else return e2.Curr.X < e1.Curr.X;
		}
		//------------------------------------------------------------------------------

		private bool IsEvenOddFillType(TEdge edge)
		{
			if (edge.PolyTyp == PolyType.ptSubject)
				return m_SubjFillType == PolyFillType.pftEvenOdd;
			else
				return m_ClipFillType == PolyFillType.pftEvenOdd;
		}
		//------------------------------------------------------------------------------

		private bool IsEvenOddAltFillType(TEdge edge)
		{
			if (edge.PolyTyp == PolyType.ptSubject)
				return m_ClipFillType == PolyFillType.pftEvenOdd;
			else
				return m_SubjFillType == PolyFillType.pftEvenOdd;
		}
		//------------------------------------------------------------------------------

		private bool IsContributing(TEdge edge)
		{
			PolyFillType pft, pft2;
			if (edge.PolyTyp == PolyType.ptSubject)
			{
				pft = m_SubjFillType;
				pft2 = m_ClipFillType;
			}
			else
			{
				pft = m_ClipFillType;
				pft2 = m_SubjFillType;
			}

			switch (pft)
			{
				case PolyFillType.pftEvenOdd:
					//return false if a subj line has been flagged as inside a subj polygon
					if (edge.WindDelta == 0 && edge.WindCnt != 1) return false;
					break;
				case PolyFillType.pftNonZero:
					if (Math.Abs(edge.WindCnt) != 1) return false;
					break;
				case PolyFillType.pftPositive:
					if (edge.WindCnt != 1) return false;
					break;
				default: //PolyFillType.pftNegative
					if (edge.WindCnt != -1) return false;
					break;
			}

			switch (m_ClipType)
			{
				case ClipType.ctIntersection:
					switch (pft2)
					{
						case PolyFillType.pftEvenOdd:
						case PolyFillType.pftNonZero:
							return (edge.WindCnt2 != 0);
						case PolyFillType.pftPositive:
							return (edge.WindCnt2 > 0);
						default:
							return (edge.WindCnt2 < 0);
					}
				case ClipType.ctUnion:
					switch (pft2)
					{
						case PolyFillType.pftEvenOdd:
						case PolyFillType.pftNonZero:
							return (edge.WindCnt2 == 0);
						case PolyFillType.pftPositive:
							return (edge.WindCnt2 <= 0);
						default:
							return (edge.WindCnt2 >= 0);
					}
				case ClipType.ctDifference:
					if (edge.PolyTyp == PolyType.ptSubject)
						switch (pft2)
						{
							case PolyFillType.pftEvenOdd:
							case PolyFillType.pftNonZero:
								return (edge.WindCnt2 == 0);
							case PolyFillType.pftPositive:
								return (edge.WindCnt2 <= 0);
							default:
								return (edge.WindCnt2 >= 0);
						}
					else
						switch (pft2)
						{
							case PolyFillType.pftEvenOdd:
							case PolyFillType.pftNonZero:
								return (edge.WindCnt2 != 0);
							case PolyFillType.pftPositive:
								return (edge.WindCnt2 > 0);
							default:
								return (edge.WindCnt2 < 0);
						}
				case ClipType.ctXor:
					if (edge.WindDelta == 0) //XOr always contributing unless open
						switch (pft2)
						{
							case PolyFillType.pftEvenOdd:
							case PolyFillType.pftNonZero:
								return (edge.WindCnt2 == 0);
							case PolyFillType.pftPositive:
								return (edge.WindCnt2 <= 0);
							default:
								return (edge.WindCnt2 >= 0);
						}
					else
						return true;
			}
			return true;
		}
		//------------------------------------------------------------------------------

		private void SetWindingCount(TEdge edge)
		{
			TEdge e = edge.PrevInAEL;
			//find the edge of the same polytype that immediately preceeds 'edge' in AEL
			while (e != null && ((e.PolyTyp != edge.PolyTyp) || (e.WindDelta == 0))) e = e.PrevInAEL;
			if (e == null)
			{
				PolyFillType pft;
				pft = (edge.PolyTyp == PolyType.ptSubject ? m_SubjFillType : m_ClipFillType);
				if (edge.WindDelta == 0) edge.WindCnt = (pft == PolyFillType.pftNegative ? -1 : 1);
				else edge.WindCnt = edge.WindDelta;
				edge.WindCnt2 = 0;
				e = m_ActiveEdges; //ie get ready to calc WindCnt2
			}
			else if (edge.WindDelta == 0 && m_ClipType != ClipType.ctUnion)
			{
				edge.WindCnt = 1;
				edge.WindCnt2 = e.WindCnt2;
				e = e.NextInAEL; //ie get ready to calc WindCnt2
			}
			else if (IsEvenOddFillType(edge))
			{
				//EvenOdd filling ...
				if (edge.WindDelta == 0)
				{
					//are we inside a subj polygon ...
					bool Inside = true;
					TEdge e2 = e.PrevInAEL;
					while (e2 != null)
					{
						if (e2.PolyTyp == e.PolyTyp && e2.WindDelta != 0)
							Inside = !Inside;
						e2 = e2.PrevInAEL;
					}
					edge.WindCnt = (Inside ? 0 : 1);
				}
				else
				{
					edge.WindCnt = edge.WindDelta;
				}
				edge.WindCnt2 = e.WindCnt2;
				e = e.NextInAEL; //ie get ready to calc WindCnt2
			}
			else
			{
				//nonZero, Positive or Negative filling ...
				if (e.WindCnt * e.WindDelta < 0)
				{
					//prev edge is 'decreasing' WindCount (WC) toward zero
					//so we're outside the previous polygon ...
					if (Math.Abs(e.WindCnt) > 1)
					{
						//outside prev poly but still inside another.
						//when reversing direction of prev poly use the same WC 
						if (e.WindDelta * edge.WindDelta < 0) edge.WindCnt = e.WindCnt;
						//otherwise continue to 'decrease' WC ...
						else edge.WindCnt = e.WindCnt + edge.WindDelta;
					}
					else
						//now outside all polys of same polytype so set own WC ...
						edge.WindCnt = (edge.WindDelta == 0 ? 1 : edge.WindDelta);
				}
				else
				{
					//prev edge is 'increasing' WindCount (WC) away from zero
					//so we're inside the previous polygon ...
					if (edge.WindDelta == 0)
						edge.WindCnt = (e.WindCnt < 0 ? e.WindCnt - 1 : e.WindCnt + 1);
					//if wind direction is reversing prev then use same WC
					else if (e.WindDelta * edge.WindDelta < 0)
						edge.WindCnt = e.WindCnt;
					//otherwise add to WC ...
					else edge.WindCnt = e.WindCnt + edge.WindDelta;
				}
				edge.WindCnt2 = e.WindCnt2;
				e = e.NextInAEL; //ie get ready to calc WindCnt2
			}

			//update WindCnt2 ...
			if (IsEvenOddAltFillType(edge))
			{
				//EvenOdd filling ...
				while (e != edge)
				{
					if (e.WindDelta != 0)
						edge.WindCnt2 = (edge.WindCnt2 == 0 ? 1 : 0);
					e = e.NextInAEL;
				}
			}
			else
			{
				//nonZero, Positive or Negative filling ...
				while (e != edge)
				{
					edge.WindCnt2 += e.WindDelta;
					e = e.NextInAEL;
				}
			}
		}
		//------------------------------------------------------------------------------

		private void AddEdgeToSEL(TEdge edge)
		{
			//SEL pointers in PEdge are use to build transient lists of horizontal edges.
			//However, since we don't need to worry about processing order, all additions
			//are made to the front of the list ...
			if (m_SortedEdges == null)
			{
				m_SortedEdges = edge;
				edge.PrevInSEL = null;
				edge.NextInSEL = null;
			}
			else
			{
				edge.NextInSEL = m_SortedEdges;
				edge.PrevInSEL = null;
				m_SortedEdges.PrevInSEL = edge;
				m_SortedEdges = edge;
			}
		}
		//------------------------------------------------------------------------------

		internal Boolean PopEdgeFromSEL(out TEdge e)
		{
			//Pop edge from front of SEL (ie SEL is a FILO list)
			e = m_SortedEdges;
			if (e == null) return false;
			TEdge oldE = e;
			m_SortedEdges = e.NextInSEL;
			if (m_SortedEdges != null) m_SortedEdges.PrevInSEL = null;
			oldE.NextInSEL = null;
			oldE.PrevInSEL = null;
			return true;
		}
		//------------------------------------------------------------------------------

		private void CopyAELToSEL()
		{
			TEdge e = m_ActiveEdges;
			m_SortedEdges = e;
			while (e != null)
			{
				e.PrevInSEL = e.PrevInAEL;
				e.NextInSEL = e.NextInAEL;
				e = e.NextInAEL;
			}
		}
		//------------------------------------------------------------------------------

		private void SwapPositionsInSEL(TEdge edge1, TEdge edge2)
		{
			if (edge1.NextInSEL == null && edge1.PrevInSEL == null)
				return;
			if (edge2.NextInSEL == null && edge2.PrevInSEL == null)
				return;

			if (edge1.NextInSEL == edge2)
			{
				TEdge next = edge2.NextInSEL;
				if (next != null)
					next.PrevInSEL = edge1;
				TEdge prev = edge1.PrevInSEL;
				if (prev != null)
					prev.NextInSEL = edge2;
				edge2.PrevInSEL = prev;
				edge2.NextInSEL = edge1;
				edge1.PrevInSEL = edge2;
				edge1.NextInSEL = next;
			}
			else if (edge2.NextInSEL == edge1)
			{
				TEdge next = edge1.NextInSEL;
				if (next != null)
					next.PrevInSEL = edge2;
				TEdge prev = edge2.PrevInSEL;
				if (prev != null)
					prev.NextInSEL = edge1;
				edge1.PrevInSEL = prev;
				edge1.NextInSEL = edge2;
				edge2.PrevInSEL = edge1;
				edge2.NextInSEL = next;
			}
			else
			{
				TEdge next = edge1.NextInSEL;
				TEdge prev = edge1.PrevInSEL;
				edge1.NextInSEL = edge2.NextInSEL;
				if (edge1.NextInSEL != null)
					edge1.NextInSEL.PrevInSEL = edge1;
				edge1.PrevInSEL = edge2.PrevInSEL;
				if (edge1.PrevInSEL != null)
					edge1.PrevInSEL.NextInSEL = edge1;
				edge2.NextInSEL = next;
				if (edge2.NextInSEL != null)
					edge2.NextInSEL.PrevInSEL = edge2;
				edge2.PrevInSEL = prev;
				if (edge2.PrevInSEL != null)
					edge2.PrevInSEL.NextInSEL = edge2;
			}

			if (edge1.PrevInSEL == null)
				m_SortedEdges = edge1;
			else if (edge2.PrevInSEL == null)
				m_SortedEdges = edge2;
		}
		//------------------------------------------------------------------------------


		private void AddLocalMaxPoly(TEdge e1, TEdge e2, IntPoint pt)
		{
			AddOutPt(e1, pt);
			if (e2.WindDelta == 0) AddOutPt(e2, pt);
			if (e1.OutIdx == e2.OutIdx)
			{
				e1.OutIdx = Unassigned;
				e2.OutIdx = Unassigned;
			}
			else if (e1.OutIdx < e2.OutIdx)
				AppendPolygon(e1, e2);
			else
				AppendPolygon(e2, e1);
		}
		//------------------------------------------------------------------------------

		private OutPt AddLocalMinPoly(TEdge e1, TEdge e2, IntPoint pt)
		{
			OutPt result;
			TEdge e, prevE;
			if (IsHorizontal(e2) || (e1.Dx > e2.Dx))
			{
				result = AddOutPt(e1, pt);
				e2.OutIdx = e1.OutIdx;
				e1.Side = EdgeSide.esLeft;
				e2.Side = EdgeSide.esRight;
				e = e1;
				if (e.PrevInAEL == e2)
					prevE = e2.PrevInAEL;
				else
					prevE = e.PrevInAEL;
			}
			else
			{
				result = AddOutPt(e2, pt);
				e1.OutIdx = e2.OutIdx;
				e1.Side = EdgeSide.esRight;
				e2.Side = EdgeSide.esLeft;
				e = e2;
				if (e.PrevInAEL == e1)
					prevE = e1.PrevInAEL;
				else
					prevE = e.PrevInAEL;
			}

			if (prevE != null && prevE.OutIdx >= 0 && prevE.Top.Y < pt.Y && e.Top.Y < pt.Y)
			{
				cInt xPrev = TopX(prevE, pt.Y);
				cInt xE = TopX(e, pt.Y);
				if ((xPrev == xE) && (e.WindDelta != 0) && (prevE.WindDelta != 0) &&
				  SlopesEqual(new IntPoint(xPrev, pt.Y), prevE.Top, new IntPoint(xE, pt.Y), e.Top, m_UseFullRange))
				{
					OutPt outPt = AddOutPt(prevE, pt);
					AddJoin(result, outPt, e.Top);
				}
			}
			return result;
		}
		//------------------------------------------------------------------------------

		private OutPt AddOutPt(TEdge e, IntPoint pt)
		{
			if (e.OutIdx < 0)
			{
				OutRec outRec = CreateOutRec();
				outRec.IsOpen = (e.WindDelta == 0);
				OutPt newOp = new OutPt();
				outRec.Pts = newOp;
				newOp.Idx = outRec.Idx;
				newOp.Pt = pt;
				newOp.Next = newOp;
				newOp.Prev = newOp;
				if (!outRec.IsOpen)
					SetHoleState(e, outRec);
				e.OutIdx = outRec.Idx; //nb: do this after SetZ !
				return newOp;
			}
			else
			{
				OutRec outRec = m_PolyOuts[e.OutIdx];
				//OutRec.Pts is the 'Left-most' point & OutRec.Pts.Prev is the 'Right-most'
				OutPt op = outRec.Pts;
				bool ToFront = (e.Side == EdgeSide.esLeft);
				if (ToFront && pt == op.Pt) return op;
				else if (!ToFront && pt == op.Prev.Pt) return op.Prev;

				OutPt newOp = new OutPt();
				newOp.Idx = outRec.Idx;
				newOp.Pt = pt;
				newOp.Next = op;
				newOp.Prev = op.Prev;
				newOp.Prev.Next = newOp;
				op.Prev = newOp;
				if (ToFront) outRec.Pts = newOp;
				return newOp;
			}
		}
		//------------------------------------------------------------------------------

		private OutPt GetLastOutPt(TEdge e)
		{
			OutRec outRec = m_PolyOuts[e.OutIdx];
			if (e.Side == EdgeSide.esLeft)
				return outRec.Pts;
			else
				return outRec.Pts.Prev;
		}
		//------------------------------------------------------------------------------

		internal void SwapPoints(ref IntPoint pt1, ref IntPoint pt2)
		{
			IntPoint tmp = new IntPoint(pt1);
			pt1 = pt2;
			pt2 = tmp;
		}
		//------------------------------------------------------------------------------

		private bool HorzSegmentsOverlap(cInt seg1a, cInt seg1b, cInt seg2a, cInt seg2b)
		{
			if (seg1a > seg1b) Swap(ref seg1a, ref seg1b);
			if (seg2a > seg2b) Swap(ref seg2a, ref seg2b);
			return (seg1a < seg2b) && (seg2a < seg1b);
		}
		//------------------------------------------------------------------------------

		private void SetHoleState(TEdge e, OutRec outRec)
		{
			TEdge e2 = e.PrevInAEL;
			TEdge eTmp = null;
			while (e2 != null)
			{
				if (e2.OutIdx >= 0 && e2.WindDelta != 0)
				{
					if (eTmp == null)
						eTmp = e2;
					else if (eTmp.OutIdx == e2.OutIdx)
						eTmp = null; //paired               
				}
				e2 = e2.PrevInAEL;
			}

			if (eTmp == null)
			{
				outRec.FirstLeft = null;
				outRec.IsHole = false;
			}
			else
			{
				outRec.FirstLeft = m_PolyOuts[eTmp.OutIdx];
				outRec.IsHole = !outRec.FirstLeft.IsHole;
			}
		}
		//------------------------------------------------------------------------------

		private double GetDx(IntPoint pt1, IntPoint pt2)
		{
			if (pt1.Y == pt2.Y) return horizontal;
			else return (double)(pt2.X - pt1.X) / (pt2.Y - pt1.Y);
		}
		//---------------------------------------------------------------------------

		private bool FirstIsBottomPt(OutPt btmPt1, OutPt btmPt2)
		{
			OutPt p = btmPt1.Prev;
			while ((p.Pt == btmPt1.Pt) && (p != btmPt1)) p = p.Prev;
			double dx1p = Math.Abs(GetDx(btmPt1.Pt, p.Pt));
			p = btmPt1.Next;
			while ((p.Pt == btmPt1.Pt) && (p != btmPt1)) p = p.Next;
			double dx1n = Math.Abs(GetDx(btmPt1.Pt, p.Pt));

			p = btmPt2.Prev;
			while ((p.Pt == btmPt2.Pt) && (p != btmPt2)) p = p.Prev;
			double dx2p = Math.Abs(GetDx(btmPt2.Pt, p.Pt));
			p = btmPt2.Next;
			while ((p.Pt == btmPt2.Pt) && (p != btmPt2)) p = p.Next;
			double dx2n = Math.Abs(GetDx(btmPt2.Pt, p.Pt));

			if (Math.Max(dx1p, dx1n) == Math.Max(dx2p, dx2n) &&
			  Math.Min(dx1p, dx1n) == Math.Min(dx2p, dx2n))
				return Area(btmPt1) > 0; //if otherwise identical use orientation
			else
				return (dx1p >= dx2p && dx1p >= dx2n) || (dx1n >= dx2p && dx1n >= dx2n);
		}
		//------------------------------------------------------------------------------

		private OutPt GetBottomPt(OutPt pp)
		{
			OutPt dups = null;
			OutPt p = pp.Next;
			while (p != pp)
			{
				if (p.Pt.Y > pp.Pt.Y)
				{
					pp = p;
					dups = null;
				}
				else if (p.Pt.Y == pp.Pt.Y && p.Pt.X <= pp.Pt.X)
				{
					if (p.Pt.X < pp.Pt.X)
					{
						dups = null;
						pp = p;
					}
					else
					{
						if (p.Next != pp && p.Prev != pp) dups = p;
					}
				}
				p = p.Next;
			}
			if (dups != null)
			{
				//there appears to be at least 2 vertices at bottomPt so ...
				while (dups != p)
				{
					if (!FirstIsBottomPt(p, dups)) pp = dups;
					dups = dups.Next;
					while (dups.Pt != pp.Pt) dups = dups.Next;
				}
			}
			return pp;
		}
		//------------------------------------------------------------------------------

		private OutRec GetLowermostRec(OutRec outRec1, OutRec outRec2)
		{
			//work out which polygon fragment has the correct hole state ...
			if (outRec1.BottomPt == null)
				outRec1.BottomPt = GetBottomPt(outRec1.Pts);
			if (outRec2.BottomPt == null)
				outRec2.BottomPt = GetBottomPt(outRec2.Pts);
			OutPt bPt1 = outRec1.BottomPt;
			OutPt bPt2 = outRec2.BottomPt;
			if (bPt1.Pt.Y > bPt2.Pt.Y) return outRec1;
			else if (bPt1.Pt.Y < bPt2.Pt.Y) return outRec2;
			else if (bPt1.Pt.X < bPt2.Pt.X) return outRec1;
			else if (bPt1.Pt.X > bPt2.Pt.X) return outRec2;
			else if (bPt1.Next == bPt1) return outRec2;
			else if (bPt2.Next == bPt2) return outRec1;
			else if (FirstIsBottomPt(bPt1, bPt2)) return outRec1;
			else return outRec2;
		}
		//------------------------------------------------------------------------------

		bool OutRec1RightOfOutRec2(OutRec outRec1, OutRec outRec2)
		{
			do
			{
				outRec1 = outRec1.FirstLeft;
				if (outRec1 == outRec2) return true;
			} while (outRec1 != null);
			return false;
		}
		//------------------------------------------------------------------------------

		private OutRec GetOutRec(int idx)
		{
			OutRec outrec = m_PolyOuts[idx];
			while (outrec != m_PolyOuts[outrec.Idx])
				outrec = m_PolyOuts[outrec.Idx];
			return outrec;
		}
		//------------------------------------------------------------------------------

		private void AppendPolygon(TEdge e1, TEdge e2)
		{
			OutRec outRec1 = m_PolyOuts[e1.OutIdx];
			OutRec outRec2 = m_PolyOuts[e2.OutIdx];

			OutRec holeStateRec;
			if (OutRec1RightOfOutRec2(outRec1, outRec2))
				holeStateRec = outRec2;
			else if (OutRec1RightOfOutRec2(outRec2, outRec1))
				holeStateRec = outRec1;
			else
				holeStateRec = GetLowermostRec(outRec1, outRec2);

			//get the start and ends of both output polygons and
			//join E2 poly onto E1 poly and delete pointers to E2 ...
			OutPt p1_lft = outRec1.Pts;
			OutPt p1_rt = p1_lft.Prev;
			OutPt p2_lft = outRec2.Pts;
			OutPt p2_rt = p2_lft.Prev;

			//join e2 poly onto e1 poly and delete pointers to e2 ...
			if (e1.Side == EdgeSide.esLeft)
			{
				if (e2.Side == EdgeSide.esLeft)
				{
					//z y x a b c
					ReversePolyPtLinks(p2_lft);
					p2_lft.Next = p1_lft;
					p1_lft.Prev = p2_lft;
					p1_rt.Next = p2_rt;
					p2_rt.Prev = p1_rt;
					outRec1.Pts = p2_rt;
				}
				else
				{
					//x y z a b c
					p2_rt.Next = p1_lft;
					p1_lft.Prev = p2_rt;
					p2_lft.Prev = p1_rt;
					p1_rt.Next = p2_lft;
					outRec1.Pts = p2_lft;
				}
			}
			else
			{
				if (e2.Side == EdgeSide.esRight)
				{
					//a b c z y x
					ReversePolyPtLinks(p2_lft);
					p1_rt.Next = p2_rt;
					p2_rt.Prev = p1_rt;
					p2_lft.Next = p1_lft;
					p1_lft.Prev = p2_lft;
				}
				else
				{
					//a b c x y z
					p1_rt.Next = p2_lft;
					p2_lft.Prev = p1_rt;
					p1_lft.Prev = p2_rt;
					p2_rt.Next = p1_lft;
				}
			}

			outRec1.BottomPt = null;
			if (holeStateRec == outRec2)
			{
				if (outRec2.FirstLeft != outRec1)
					outRec1.FirstLeft = outRec2.FirstLeft;
				outRec1.IsHole = outRec2.IsHole;
			}
			outRec2.Pts = null;
			outRec2.BottomPt = null;

			outRec2.FirstLeft = outRec1;

			int OKIdx = e1.OutIdx;
			int ObsoleteIdx = e2.OutIdx;

			e1.OutIdx = Unassigned; //nb: safe because we only get here via AddLocalMaxPoly
			e2.OutIdx = Unassigned;

			TEdge e = m_ActiveEdges;
			while (e != null)
			{
				if (e.OutIdx == ObsoleteIdx)
				{
					e.OutIdx = OKIdx;
					e.Side = e1.Side;
					break;
				}
				e = e.NextInAEL;
			}
			outRec2.Idx = outRec1.Idx;
		}
		//------------------------------------------------------------------------------

		private void ReversePolyPtLinks(OutPt pp)
		{
			if (pp == null) return;
			OutPt pp1;
			OutPt pp2;
			pp1 = pp;
			do
			{
				pp2 = pp1.Next;
				pp1.Next = pp1.Prev;
				pp1.Prev = pp2;
				pp1 = pp2;
			} while (pp1 != pp);
		}
		//------------------------------------------------------------------------------

		private static void SwapSides(TEdge edge1, TEdge edge2)
		{
			EdgeSide side = edge1.Side;
			edge1.Side = edge2.Side;
			edge2.Side = side;
		}
		//------------------------------------------------------------------------------

		private static void SwapPolyIndexes(TEdge edge1, TEdge edge2)
		{
			int outIdx = edge1.OutIdx;
			edge1.OutIdx = edge2.OutIdx;
			edge2.OutIdx = outIdx;
		}
		//------------------------------------------------------------------------------

		private void IntersectEdges(TEdge e1, TEdge e2, IntPoint pt)
		{
			//e1 will be to the left of e2 BELOW the intersection. Therefore e1 is before
			//e2 in AEL except when e1 is being inserted at the intersection point ...

			bool e1Contributing = (e1.OutIdx >= 0);
			bool e2Contributing = (e2.OutIdx >= 0);

#if use_xyz
          SetZ(ref pt, e1, e2);
#endif

#if use_lines
			//if either edge is on an OPEN path ...
			if (e1.WindDelta == 0 || e2.WindDelta == 0)
			{
				//ignore subject-subject open path intersections UNLESS they
				//are both open paths, AND they are both 'contributing maximas' ...
				if (e1.WindDelta == 0 && e2.WindDelta == 0) return;
				//if intersecting a subj line with a subj poly ...
				else if (e1.PolyTyp == e2.PolyTyp &&
				  e1.WindDelta != e2.WindDelta && m_ClipType == ClipType.ctUnion)
				{
					if (e1.WindDelta == 0)
					{
						if (e2Contributing)
						{
							AddOutPt(e1, pt);
							if (e1Contributing) e1.OutIdx = Unassigned;
						}
					}
					else
					{
						if (e1Contributing)
						{
							AddOutPt(e2, pt);
							if (e2Contributing) e2.OutIdx = Unassigned;
						}
					}
				}
				else if (e1.PolyTyp != e2.PolyTyp)
				{
					if ((e1.WindDelta == 0) && Math.Abs(e2.WindCnt) == 1 &&
					  (m_ClipType != ClipType.ctUnion || e2.WindCnt2 == 0))
					{
						AddOutPt(e1, pt);
						if (e1Contributing) e1.OutIdx = Unassigned;
					}
					else if ((e2.WindDelta == 0) && (Math.Abs(e1.WindCnt) == 1) &&
					  (m_ClipType != ClipType.ctUnion || e1.WindCnt2 == 0))
					{
						AddOutPt(e2, pt);
						if (e2Contributing) e2.OutIdx = Unassigned;
					}
				}
				return;
			}
#endif

			//update winding counts...
			//assumes that e1 will be to the Right of e2 ABOVE the intersection
			if (e1.PolyTyp == e2.PolyTyp)
			{
				if (IsEvenOddFillType(e1))
				{
					int oldE1WindCnt = e1.WindCnt;
					e1.WindCnt = e2.WindCnt;
					e2.WindCnt = oldE1WindCnt;
				}
				else
				{
					if (e1.WindCnt + e2.WindDelta == 0) e1.WindCnt = -e1.WindCnt;
					else e1.WindCnt += e2.WindDelta;
					if (e2.WindCnt - e1.WindDelta == 0) e2.WindCnt = -e2.WindCnt;
					else e2.WindCnt -= e1.WindDelta;
				}
			}
			else
			{
				if (!IsEvenOddFillType(e2)) e1.WindCnt2 += e2.WindDelta;
				else e1.WindCnt2 = (e1.WindCnt2 == 0) ? 1 : 0;
				if (!IsEvenOddFillType(e1)) e2.WindCnt2 -= e1.WindDelta;
				else e2.WindCnt2 = (e2.WindCnt2 == 0) ? 1 : 0;
			}

			PolyFillType e1FillType, e2FillType, e1FillType2, e2FillType2;
			if (e1.PolyTyp == PolyType.ptSubject)
			{
				e1FillType = m_SubjFillType;
				e1FillType2 = m_ClipFillType;
			}
			else
			{
				e1FillType = m_ClipFillType;
				e1FillType2 = m_SubjFillType;
			}
			if (e2.PolyTyp == PolyType.ptSubject)
			{
				e2FillType = m_SubjFillType;
				e2FillType2 = m_ClipFillType;
			}
			else
			{
				e2FillType = m_ClipFillType;
				e2FillType2 = m_SubjFillType;
			}

			int e1Wc, e2Wc;
			switch (e1FillType)
			{
				case PolyFillType.pftPositive: e1Wc = e1.WindCnt; break;
				case PolyFillType.pftNegative: e1Wc = -e1.WindCnt; break;
				default: e1Wc = Math.Abs(e1.WindCnt); break;
			}
			switch (e2FillType)
			{
				case PolyFillType.pftPositive: e2Wc = e2.WindCnt; break;
				case PolyFillType.pftNegative: e2Wc = -e2.WindCnt; break;
				default: e2Wc = Math.Abs(e2.WindCnt); break;
			}

			if (e1Contributing && e2Contributing)
			{
				if ((e1Wc != 0 && e1Wc != 1) || (e2Wc != 0 && e2Wc != 1) ||
				  (e1.PolyTyp != e2.PolyTyp && m_ClipType != ClipType.ctXor))
				{
					AddLocalMaxPoly(e1, e2, pt);
				}
				else
				{
					AddOutPt(e1, pt);
					AddOutPt(e2, pt);
					SwapSides(e1, e2);
					SwapPolyIndexes(e1, e2);
				}
			}
			else if (e1Contributing)
			{
				if (e2Wc == 0 || e2Wc == 1)
				{
					AddOutPt(e1, pt);
					SwapSides(e1, e2);
					SwapPolyIndexes(e1, e2);
				}

			}
			else if (e2Contributing)
			{
				if (e1Wc == 0 || e1Wc == 1)
				{
					AddOutPt(e2, pt);
					SwapSides(e1, e2);
					SwapPolyIndexes(e1, e2);
				}
			}
			else if ((e1Wc == 0 || e1Wc == 1) && (e2Wc == 0 || e2Wc == 1))
			{
				//neither edge is currently contributing ...
				cInt e1Wc2, e2Wc2;
				switch (e1FillType2)
				{
					case PolyFillType.pftPositive: e1Wc2 = e1.WindCnt2; break;
					case PolyFillType.pftNegative: e1Wc2 = -e1.WindCnt2; break;
					default: e1Wc2 = Math.Abs(e1.WindCnt2); break;
				}
				switch (e2FillType2)
				{
					case PolyFillType.pftPositive: e2Wc2 = e2.WindCnt2; break;
					case PolyFillType.pftNegative: e2Wc2 = -e2.WindCnt2; break;
					default: e2Wc2 = Math.Abs(e2.WindCnt2); break;
				}

				if (e1.PolyTyp != e2.PolyTyp)
				{
					AddLocalMinPoly(e1, e2, pt);
				}
				else if (e1Wc == 1 && e2Wc == 1)
					switch (m_ClipType)
					{
						case ClipType.ctIntersection:
							if (e1Wc2 > 0 && e2Wc2 > 0)
								AddLocalMinPoly(e1, e2, pt);
							break;
						case ClipType.ctUnion:
							if (e1Wc2 <= 0 && e2Wc2 <= 0)
								AddLocalMinPoly(e1, e2, pt);
							break;
						case ClipType.ctDifference:
							if (((e1.PolyTyp == PolyType.ptClip) && (e1Wc2 > 0) && (e2Wc2 > 0)) ||
								((e1.PolyTyp == PolyType.ptSubject) && (e1Wc2 <= 0) && (e2Wc2 <= 0)))
								AddLocalMinPoly(e1, e2, pt);
							break;
						case ClipType.ctXor:
							AddLocalMinPoly(e1, e2, pt);
							break;
					}
				else
					SwapSides(e1, e2);
			}
		}
		//------------------------------------------------------------------------------

		private void DeleteFromSEL(TEdge e)
		{
			TEdge SelPrev = e.PrevInSEL;
			TEdge SelNext = e.NextInSEL;
			if (SelPrev == null && SelNext == null && (e != m_SortedEdges))
				return; //already deleted
			if (SelPrev != null)
				SelPrev.NextInSEL = SelNext;
			else m_SortedEdges = SelNext;
			if (SelNext != null)
				SelNext.PrevInSEL = SelPrev;
			e.NextInSEL = null;
			e.PrevInSEL = null;
		}
		//------------------------------------------------------------------------------

		private void ProcessHorizontals()
		{
			TEdge horzEdge; //m_SortedEdges;
			while (PopEdgeFromSEL(out horzEdge))
				ProcessHorizontal(horzEdge);
		}
		//------------------------------------------------------------------------------

		void GetHorzDirection(TEdge HorzEdge, out Direction Dir, out cInt Left, out cInt Right)
		{
			if (HorzEdge.Bot.X < HorzEdge.Top.X)
			{
				Left = HorzEdge.Bot.X;
				Right = HorzEdge.Top.X;
				Dir = Direction.dLeftToRight;
			}
			else
			{
				Left = HorzEdge.Top.X;
				Right = HorzEdge.Bot.X;
				Dir = Direction.dRightToLeft;
			}
		}
		//------------------------------------------------------------------------

		private void ProcessHorizontal(TEdge horzEdge)
		{
			Direction dir;
			cInt horzLeft, horzRight;
			bool IsOpen = horzEdge.WindDelta == 0;

			GetHorzDirection(horzEdge, out dir, out horzLeft, out horzRight);

			TEdge eLastHorz = horzEdge, eMaxPair = null;
			while (eLastHorz.NextInLML != null && IsHorizontal(eLastHorz.NextInLML))
				eLastHorz = eLastHorz.NextInLML;
			if (eLastHorz.NextInLML == null)
				eMaxPair = GetMaximaPair(eLastHorz);

			Maxima currMax = m_Maxima;
			if (currMax != null)
			{
				//get the first maxima in range (X) ...
				if (dir == Direction.dLeftToRight)
				{
					while (currMax != null && currMax.X <= horzEdge.Bot.X)
						currMax = currMax.Next;
					if (currMax != null && currMax.X >= eLastHorz.Top.X)
						currMax = null;
				}
				else
				{
					while (currMax.Next != null && currMax.Next.X < horzEdge.Bot.X)
						currMax = currMax.Next;
					if (currMax.X <= eLastHorz.Top.X) currMax = null;
				}
			}

			OutPt op1 = null;
			for (; ; ) //loop through consec. horizontal edges
			{
				bool IsLastHorz = (horzEdge == eLastHorz);
				TEdge e = GetNextInAEL(horzEdge, dir);
				while (e != null)
				{

					//this code block inserts extra coords into horizontal edges (in output
					//polygons) whereever maxima touch these horizontal edges. This helps
					//'simplifying' polygons (ie if the Simplify property is set).
					if (currMax != null)
					{
						if (dir == Direction.dLeftToRight)
						{
							while (currMax != null && currMax.X < e.Curr.X)
							{
								if (horzEdge.OutIdx >= 0 && !IsOpen)
									AddOutPt(horzEdge, new IntPoint(currMax.X, horzEdge.Bot.Y));
								currMax = currMax.Next;
							}
						}
						else
						{
							while (currMax != null && currMax.X > e.Curr.X)
							{
								if (horzEdge.OutIdx >= 0 && !IsOpen)
									AddOutPt(horzEdge, new IntPoint(currMax.X, horzEdge.Bot.Y));
								currMax = currMax.Prev;
							}
						}
					};

					if ((dir == Direction.dLeftToRight && e.Curr.X > horzRight) ||
					  (dir == Direction.dRightToLeft && e.Curr.X < horzLeft)) break;

					//Also break if we've got to the end of an intermediate horizontal edge ...
					//nb: Smaller Dx's are to the right of larger Dx's ABOVE the horizontal.
					if (e.Curr.X == horzEdge.Top.X && horzEdge.NextInLML != null &&
					  e.Dx < horzEdge.NextInLML.Dx) break;

					if (horzEdge.OutIdx >= 0 && !IsOpen)  //note: may be done multiple times
					{
#if use_xyz
                  if (dir == Direction.dLeftToRight) SetZ(ref e.Curr, horzEdge, e);
                  else SetZ(ref e.Curr, e, horzEdge);
#endif

						op1 = AddOutPt(horzEdge, e.Curr);
						TEdge eNextHorz = m_SortedEdges;
						while (eNextHorz != null)
						{
							if (eNextHorz.OutIdx >= 0 &&
							  HorzSegmentsOverlap(horzEdge.Bot.X,
							  horzEdge.Top.X, eNextHorz.Bot.X, eNextHorz.Top.X))
							{
								OutPt op2 = GetLastOutPt(eNextHorz);
								AddJoin(op2, op1, eNextHorz.Top);
							}
							eNextHorz = eNextHorz.NextInSEL;
						}
						AddGhostJoin(op1, horzEdge.Bot);
					}

					//OK, so far we're still in range of the horizontal Edge  but make sure
					//we're at the last of consec. horizontals when matching with eMaxPair
					if (e == eMaxPair && IsLastHorz)
					{
						if (horzEdge.OutIdx >= 0)
							AddLocalMaxPoly(horzEdge, eMaxPair, horzEdge.Top);
						DeleteFromAEL(horzEdge);
						DeleteFromAEL(eMaxPair);
						return;
					}

					if (dir == Direction.dLeftToRight)
					{
						IntPoint Pt = new IntPoint(e.Curr.X, horzEdge.Curr.Y);
						IntersectEdges(horzEdge, e, Pt);
					}
					else
					{
						IntPoint Pt = new IntPoint(e.Curr.X, horzEdge.Curr.Y);
						IntersectEdges(e, horzEdge, Pt);
					}
					TEdge eNext = GetNextInAEL(e, dir);
					SwapPositionsInAEL(horzEdge, e);
					e = eNext;
				} //end while(e != null)

				//Break out of loop if HorzEdge.NextInLML is not also horizontal ...
				if (horzEdge.NextInLML == null || !IsHorizontal(horzEdge.NextInLML)) break;

				UpdateEdgeIntoAEL(ref horzEdge);
				if (horzEdge.OutIdx >= 0) AddOutPt(horzEdge, horzEdge.Bot);
				GetHorzDirection(horzEdge, out dir, out horzLeft, out horzRight);

			} //end for (;;)

			if (horzEdge.OutIdx >= 0 && op1 == null)
			{
				op1 = GetLastOutPt(horzEdge);
				TEdge eNextHorz = m_SortedEdges;
				while (eNextHorz != null)
				{
					if (eNextHorz.OutIdx >= 0 &&
					  HorzSegmentsOverlap(horzEdge.Bot.X,
					  horzEdge.Top.X, eNextHorz.Bot.X, eNextHorz.Top.X))
					{
						OutPt op2 = GetLastOutPt(eNextHorz);
						AddJoin(op2, op1, eNextHorz.Top);
					}
					eNextHorz = eNextHorz.NextInSEL;
				}
				AddGhostJoin(op1, horzEdge.Top);
			}

			if (horzEdge.NextInLML != null)
			{
				if (horzEdge.OutIdx >= 0)
				{
					op1 = AddOutPt(horzEdge, horzEdge.Top);

					UpdateEdgeIntoAEL(ref horzEdge);
					if (horzEdge.WindDelta == 0) return;
					//nb: HorzEdge is no longer horizontal here
					TEdge ePrev = horzEdge.PrevInAEL;
					TEdge eNext = horzEdge.NextInAEL;
					if (ePrev != null && ePrev.Curr.X == horzEdge.Bot.X &&
					  ePrev.Curr.Y == horzEdge.Bot.Y && ePrev.WindDelta != 0 &&
					  (ePrev.OutIdx >= 0 && ePrev.Curr.Y > ePrev.Top.Y &&
					  SlopesEqual(horzEdge, ePrev, m_UseFullRange)))
					{
						OutPt op2 = AddOutPt(ePrev, horzEdge.Bot);
						AddJoin(op1, op2, horzEdge.Top);
					}
					else if (eNext != null && eNext.Curr.X == horzEdge.Bot.X &&
					  eNext.Curr.Y == horzEdge.Bot.Y && eNext.WindDelta != 0 &&
					  eNext.OutIdx >= 0 && eNext.Curr.Y > eNext.Top.Y &&
					  SlopesEqual(horzEdge, eNext, m_UseFullRange))
					{
						OutPt op2 = AddOutPt(eNext, horzEdge.Bot);
						AddJoin(op1, op2, horzEdge.Top);
					}
				}
				else
					UpdateEdgeIntoAEL(ref horzEdge);
			}
			else
			{
				if (horzEdge.OutIdx >= 0) AddOutPt(horzEdge, horzEdge.Top);
				DeleteFromAEL(horzEdge);
			}
		}
		//------------------------------------------------------------------------------

		private TEdge GetNextInAEL(TEdge e, Direction Direction)
		{
			return Direction == Direction.dLeftToRight ? e.NextInAEL : e.PrevInAEL;
		}
		//------------------------------------------------------------------------------

		private bool IsMinima(TEdge e)
		{
			return e != null && (e.Prev.NextInLML != e) && (e.Next.NextInLML != e);
		}
		//------------------------------------------------------------------------------

		private bool IsMaxima(TEdge e, double Y)
		{
			return (e != null && e.Top.Y == Y && e.NextInLML == null);
		}
		//------------------------------------------------------------------------------

		private bool IsIntermediate(TEdge e, double Y)
		{
			return (e.Top.Y == Y && e.NextInLML != null);
		}
		//------------------------------------------------------------------------------

		internal TEdge GetMaximaPair(TEdge e)
		{
			if ((e.Next.Top == e.Top) && e.Next.NextInLML == null)
				return e.Next;
			else if ((e.Prev.Top == e.Top) && e.Prev.NextInLML == null)
				return e.Prev;
			else
				return null;
		}
		//------------------------------------------------------------------------------

		internal TEdge GetMaximaPairEx(TEdge e)
		{
			//as above but returns null if MaxPair isn't in AEL (unless it's horizontal)
			TEdge result = GetMaximaPair(e);
			if (result == null || result.OutIdx == Skip ||
			  ((result.NextInAEL == result.PrevInAEL) && !IsHorizontal(result))) return null;
			return result;
		}
		//------------------------------------------------------------------------------

		private bool ProcessIntersections(cInt topY)
		{
			if (m_ActiveEdges == null) return true;
			try
			{
				BuildIntersectList(topY);
				if (m_IntersectList.Count == 0) return true;
				if (m_IntersectList.Count == 1 || FixupIntersectionOrder())
					ProcessIntersectList();
				else
					return false;
			}
			catch
			{
				m_SortedEdges = null;
				m_IntersectList.Clear();
				throw new ClipperException("ProcessIntersections error");
			}
			m_SortedEdges = null;
			return true;
		}
		//------------------------------------------------------------------------------

		private void BuildIntersectList(cInt topY)
		{
			if (m_ActiveEdges == null) return;

			//prepare for sorting ...
			TEdge e = m_ActiveEdges;
			m_SortedEdges = e;
			while (e != null)
			{
				e.PrevInSEL = e.PrevInAEL;
				e.NextInSEL = e.NextInAEL;
				e.Curr.X = TopX(e, topY);
				e = e.NextInAEL;
			}

			//bubblesort ...
			bool isModified = true;
			while (isModified && m_SortedEdges != null)
			{
				isModified = false;
				e = m_SortedEdges;
				while (e.NextInSEL != null)
				{
					TEdge eNext = e.NextInSEL;
					IntPoint pt;
					if (e.Curr.X > eNext.Curr.X)
					{
						IntersectPoint(e, eNext, out pt);
						if (pt.Y < topY)
							pt = new IntPoint(TopX(e, topY), topY);
						IntersectNode newNode = new IntersectNode();
						newNode.Edge1 = e;
						newNode.Edge2 = eNext;
						newNode.Pt = pt;
						m_IntersectList.Add(newNode);

						SwapPositionsInSEL(e, eNext);
						isModified = true;
					}
					else
						e = eNext;
				}
				if (e.PrevInSEL != null) e.PrevInSEL.NextInSEL = null;
				else break;
			}
			m_SortedEdges = null;
		}
		//------------------------------------------------------------------------------

		private bool EdgesAdjacent(IntersectNode inode)
		{
			return (inode.Edge1.NextInSEL == inode.Edge2) ||
			  (inode.Edge1.PrevInSEL == inode.Edge2);
		}
		//------------------------------------------------------------------------------

		private static int IntersectNodeSort(IntersectNode node1, IntersectNode node2)
		{
			//the following typecast is safe because the differences in Pt.Y will
			//be limited to the height of the scanbeam.
			return (int)(node2.Pt.Y - node1.Pt.Y);
		}
		//------------------------------------------------------------------------------

		private bool FixupIntersectionOrder()
		{
			//pre-condition: intersections are sorted bottom-most first.
			//Now it's crucial that intersections are made only between adjacent edges,
			//so to ensure this the order of intersections may need adjusting ...
			m_IntersectList.Sort(m_IntersectNodeComparer);

			CopyAELToSEL();
			int cnt = m_IntersectList.Count;
			for (int i = 0; i < cnt; i++)
			{
				if (!EdgesAdjacent(m_IntersectList[i]))
				{
					int j = i + 1;
					while (j < cnt && !EdgesAdjacent(m_IntersectList[j])) j++;
					if (j == cnt) return false;

					IntersectNode tmp = m_IntersectList[i];
					m_IntersectList[i] = m_IntersectList[j];
					m_IntersectList[j] = tmp;

				}
				SwapPositionsInSEL(m_IntersectList[i].Edge1, m_IntersectList[i].Edge2);
			}
			return true;
		}
		//------------------------------------------------------------------------------

		private void ProcessIntersectList()
		{
			for (int i = 0; i < m_IntersectList.Count; i++)
			{
				IntersectNode iNode = m_IntersectList[i];
				{
					IntersectEdges(iNode.Edge1, iNode.Edge2, iNode.Pt);
					SwapPositionsInAEL(iNode.Edge1, iNode.Edge2);
				}
			}
			m_IntersectList.Clear();
		}
		//------------------------------------------------------------------------------

		internal static cInt Round(double value)
		{
			return value < 0 ? (cInt)(value - 0.5) : (cInt)(value + 0.5);
		}
		//------------------------------------------------------------------------------

		private static cInt TopX(TEdge edge, cInt currentY)
		{
			if (currentY == edge.Top.Y)
				return edge.Top.X;
			return edge.Bot.X + Round(edge.Dx * (currentY - edge.Bot.Y));
		}
		//------------------------------------------------------------------------------

		private void IntersectPoint(TEdge edge1, TEdge edge2, out IntPoint ip)
		{
			ip = new IntPoint();
			double b1, b2;
			//nb: with very large coordinate values, it's possible for SlopesEqual() to 
			//return false but for the edge.Dx value be equal due to double precision rounding.
			if (edge1.Dx == edge2.Dx)
			{
				ip.Y = edge1.Curr.Y;
				ip.X = TopX(edge1, ip.Y);
				return;
			}

			if (edge1.Delta.X == 0)
			{
				ip.X = edge1.Bot.X;
				if (IsHorizontal(edge2))
				{
					ip.Y = edge2.Bot.Y;
				}
				else
				{
					b2 = edge2.Bot.Y - (edge2.Bot.X / edge2.Dx);
					ip.Y = Round(ip.X / edge2.Dx + b2);
				}
			}
			else if (edge2.Delta.X == 0)
			{
				ip.X = edge2.Bot.X;
				if (IsHorizontal(edge1))
				{
					ip.Y = edge1.Bot.Y;
				}
				else
				{
					b1 = edge1.Bot.Y - (edge1.Bot.X / edge1.Dx);
					ip.Y = Round(ip.X / edge1.Dx + b1);
				}
			}
			else
			{
				b1 = edge1.Bot.X - edge1.Bot.Y * edge1.Dx;
				b2 = edge2.Bot.X - edge2.Bot.Y * edge2.Dx;
				double q = (b2 - b1) / (edge1.Dx - edge2.Dx);
				ip.Y = Round(q);
				if (Math.Abs(edge1.Dx) < Math.Abs(edge2.Dx))
					ip.X = Round(edge1.Dx * q + b1);
				else
					ip.X = Round(edge2.Dx * q + b2);
			}

			if (ip.Y < edge1.Top.Y || ip.Y < edge2.Top.Y)
			{
				if (edge1.Top.Y > edge2.Top.Y)
					ip.Y = edge1.Top.Y;
				else
					ip.Y = edge2.Top.Y;
				if (Math.Abs(edge1.Dx) < Math.Abs(edge2.Dx))
					ip.X = TopX(edge1, ip.Y);
				else
					ip.X = TopX(edge2, ip.Y);
			}
			//finally, don't allow 'ip' to be BELOW curr.Y (ie bottom of scanbeam) ...
			if (ip.Y > edge1.Curr.Y)
			{
				ip.Y = edge1.Curr.Y;
				//better to use the more vertical edge to derive X ...
				if (Math.Abs(edge1.Dx) > Math.Abs(edge2.Dx))
					ip.X = TopX(edge2, ip.Y);
				else
					ip.X = TopX(edge1, ip.Y);
			}
		}
		//------------------------------------------------------------------------------

		private void ProcessEdgesAtTopOfScanbeam(cInt topY)
		{
			TEdge e = m_ActiveEdges;
			while (e != null)
			{
				//1. process maxima, treating them as if they're 'bent' horizontal edges,
				//   but exclude maxima with horizontal edges. nb: e can't be a horizontal.
				bool IsMaximaEdge = IsMaxima(e, topY);

				if (IsMaximaEdge)
				{
					TEdge eMaxPair = GetMaximaPairEx(e);
					IsMaximaEdge = (eMaxPair == null || !IsHorizontal(eMaxPair));
				}

				if (IsMaximaEdge)
				{
					if (StrictlySimple) InsertMaxima(e.Top.X);
					TEdge ePrev = e.PrevInAEL;
					DoMaxima(e);
					if (ePrev == null) e = m_ActiveEdges;
					else e = ePrev.NextInAEL;
				}
				else
				{
					//2. promote horizontal edges, otherwise update Curr.X and Curr.Y ...
					if (IsIntermediate(e, topY) && IsHorizontal(e.NextInLML))
					{
						UpdateEdgeIntoAEL(ref e);
						if (e.OutIdx >= 0)
							AddOutPt(e, e.Bot);
						AddEdgeToSEL(e);
					}
					else
					{
						e.Curr.X = TopX(e, topY);
						e.Curr.Y = topY;
#if use_xyz
              if (e.Top.Y == topY) e.Curr.Z = e.Top.Z;
              else if (e.Bot.Y == topY) e.Curr.Z = e.Bot.Z;
              else e.Curr.Z = 0;
#endif
					}
					//When StrictlySimple and 'e' is being touched by another edge, then
					//make sure both edges have a vertex here ...
					if (StrictlySimple)
					{
						TEdge ePrev = e.PrevInAEL;
						if ((e.OutIdx >= 0) && (e.WindDelta != 0) && ePrev != null &&
						  (ePrev.OutIdx >= 0) && (ePrev.Curr.X == e.Curr.X) &&
						  (ePrev.WindDelta != 0))
						{
							IntPoint ip = new IntPoint(e.Curr);
#if use_xyz
                SetZ(ref ip, ePrev, e);
#endif
							OutPt op = AddOutPt(ePrev, ip);
							OutPt op2 = AddOutPt(e, ip);
							AddJoin(op, op2, ip); //StrictlySimple (type-3) join
						}
					}

					e = e.NextInAEL;
				}
			}

			//3. Process horizontals at the Top of the scanbeam ...
			ProcessHorizontals();
			m_Maxima = null;

			//4. Promote intermediate vertices ...
			e = m_ActiveEdges;
			while (e != null)
			{
				if (IsIntermediate(e, topY))
				{
					OutPt op = null;
					if (e.OutIdx >= 0)
						op = AddOutPt(e, e.Top);
					UpdateEdgeIntoAEL(ref e);

					//if output polygons share an edge, they'll need joining later ...
					TEdge ePrev = e.PrevInAEL;
					TEdge eNext = e.NextInAEL;
					if (ePrev != null && ePrev.Curr.X == e.Bot.X &&
					  ePrev.Curr.Y == e.Bot.Y && op != null &&
					  ePrev.OutIdx >= 0 && ePrev.Curr.Y > ePrev.Top.Y &&
					  SlopesEqual(e.Curr, e.Top, ePrev.Curr, ePrev.Top, m_UseFullRange) &&
					  (e.WindDelta != 0) && (ePrev.WindDelta != 0))
					{
						OutPt op2 = AddOutPt(ePrev, e.Bot);
						AddJoin(op, op2, e.Top);
					}
					else if (eNext != null && eNext.Curr.X == e.Bot.X &&
					  eNext.Curr.Y == e.Bot.Y && op != null &&
					  eNext.OutIdx >= 0 && eNext.Curr.Y > eNext.Top.Y &&
					  SlopesEqual(e.Curr, e.Top, eNext.Curr, eNext.Top, m_UseFullRange) &&
					  (e.WindDelta != 0) && (eNext.WindDelta != 0))
					{
						OutPt op2 = AddOutPt(eNext, e.Bot);
						AddJoin(op, op2, e.Top);
					}
				}
				e = e.NextInAEL;
			}
		}
		//------------------------------------------------------------------------------

		private void DoMaxima(TEdge e)
		{
			TEdge eMaxPair = GetMaximaPairEx(e);
			if (eMaxPair == null)
			{
				if (e.OutIdx >= 0)
					AddOutPt(e, e.Top);
				DeleteFromAEL(e);
				return;
			}

			TEdge eNext = e.NextInAEL;
			while (eNext != null && eNext != eMaxPair)
			{
				IntersectEdges(e, eNext, e.Top);
				SwapPositionsInAEL(e, eNext);
				eNext = e.NextInAEL;
			}

			if (e.OutIdx == Unassigned && eMaxPair.OutIdx == Unassigned)
			{
				DeleteFromAEL(e);
				DeleteFromAEL(eMaxPair);
			}
			else if (e.OutIdx >= 0 && eMaxPair.OutIdx >= 0)
			{
				if (e.OutIdx >= 0) AddLocalMaxPoly(e, eMaxPair, e.Top);
				DeleteFromAEL(e);
				DeleteFromAEL(eMaxPair);
			}
#if use_lines
			else if (e.WindDelta == 0)
			{
				if (e.OutIdx >= 0)
				{
					AddOutPt(e, e.Top);
					e.OutIdx = Unassigned;
				}
				DeleteFromAEL(e);

				if (eMaxPair.OutIdx >= 0)
				{
					AddOutPt(eMaxPair, e.Top);
					eMaxPair.OutIdx = Unassigned;
				}
				DeleteFromAEL(eMaxPair);
			}
#endif
			else throw new ClipperException("DoMaxima error");
		}
		//------------------------------------------------------------------------------

		public static void ReversePaths(Paths polys)
		{
			foreach (var poly in polys) { poly.Reverse(); }
		}
		//------------------------------------------------------------------------------

		public static bool Orientation(Path poly)
		{
			return Area(poly) >= 0;
		}
		//------------------------------------------------------------------------------

		private int PointCount(OutPt pts)
		{
			if (pts == null) return 0;
			int result = 0;
			OutPt p = pts;
			do
			{
				result++;
				p = p.Next;
			}
			while (p != pts);
			return result;
		}
		//------------------------------------------------------------------------------

		private void BuildResult(Paths polyg)
		{
			polyg.Clear();
			polyg.Capacity = m_PolyOuts.Count;
			for (int i = 0; i < m_PolyOuts.Count; i++)
			{
				OutRec outRec = m_PolyOuts[i];
				if (outRec.Pts == null) continue;
				OutPt p = outRec.Pts.Prev;
				int cnt = PointCount(p);
				if (cnt < 2) continue;
				Path pg = new Path(cnt);
				for (int j = 0; j < cnt; j++)
				{
					pg.Add(p.Pt);
					p = p.Prev;
				}
				polyg.Add(pg);
			}
		}
		//------------------------------------------------------------------------------

		private void BuildResult2(PolyTree polytree)
		{
			polytree.Clear();

			//add each output polygon/contour to polytree ...
			polytree.m_AllPolys.Capacity = m_PolyOuts.Count;
			for (int i = 0; i < m_PolyOuts.Count; i++)
			{
				OutRec outRec = m_PolyOuts[i];
				int cnt = PointCount(outRec.Pts);
				if ((outRec.IsOpen && cnt < 2) ||
				  (!outRec.IsOpen && cnt < 3)) continue;
				FixHoleLinkage(outRec);
				PolyNode pn = new PolyNode();
				polytree.m_AllPolys.Add(pn);
				outRec.PolyNode = pn;
				pn.m_polygon.Capacity = cnt;
				OutPt op = outRec.Pts.Prev;
				for (int j = 0; j < cnt; j++)
				{
					pn.m_polygon.Add(op.Pt);
					op = op.Prev;
				}
			}

			//fixup PolyNode links etc ...
			polytree.m_Childs.Capacity = m_PolyOuts.Count;
			for (int i = 0; i < m_PolyOuts.Count; i++)
			{
				OutRec outRec = m_PolyOuts[i];
				if (outRec.PolyNode == null) continue;
				else if (outRec.IsOpen)
				{
					outRec.PolyNode.IsOpen = true;
					polytree.AddChild(outRec.PolyNode);
				}
				else if (outRec.FirstLeft != null &&
				  outRec.FirstLeft.PolyNode != null)
					outRec.FirstLeft.PolyNode.AddChild(outRec.PolyNode);
				else
					polytree.AddChild(outRec.PolyNode);
			}
		}
		//------------------------------------------------------------------------------

		private void FixupOutPolyline(OutRec outrec)
		{
			OutPt pp = outrec.Pts;
			OutPt lastPP = pp.Prev;
			while (pp != lastPP)
			{
				pp = pp.Next;
				if (pp.Pt == pp.Prev.Pt)
				{
					if (pp == lastPP) lastPP = pp.Prev;
					OutPt tmpPP = pp.Prev;
					tmpPP.Next = pp.Next;
					pp.Next.Prev = tmpPP;
					pp = tmpPP;
				}
			}
			if (pp == pp.Prev) outrec.Pts = null;
		}
		//------------------------------------------------------------------------------

		private void FixupOutPolygon(OutRec outRec)
		{
			//FixupOutPolygon() - removes duplicate points and simplifies consecutive
			//parallel edges by removing the middle vertex.
			OutPt lastOK = null;
			outRec.BottomPt = null;
			OutPt pp = outRec.Pts;
			bool preserveCol = PreserveCollinear || StrictlySimple;
			for (; ; )
			{
				if (pp.Prev == pp || pp.Prev == pp.Next)
				{
					outRec.Pts = null;
					return;
				}
				//test for duplicate points and collinear edges ...
				if ((pp.Pt == pp.Next.Pt) || (pp.Pt == pp.Prev.Pt) ||
				  (SlopesEqual(pp.Prev.Pt, pp.Pt, pp.Next.Pt, m_UseFullRange) &&
				  (!preserveCol || !Pt2IsBetweenPt1AndPt3(pp.Prev.Pt, pp.Pt, pp.Next.Pt))))
				{
					lastOK = null;
					pp.Prev.Next = pp.Next;
					pp.Next.Prev = pp.Prev;
					pp = pp.Prev;
				}
				else if (pp == lastOK) break;
				else
				{
					if (lastOK == null) lastOK = pp;
					pp = pp.Next;
				}
			}
			outRec.Pts = pp;
		}
		//------------------------------------------------------------------------------

		OutPt DupOutPt(OutPt outPt, bool InsertAfter)
		{
			OutPt result = new OutPt();
			result.Pt = outPt.Pt;
			result.Idx = outPt.Idx;
			if (InsertAfter)
			{
				result.Next = outPt.Next;
				result.Prev = outPt;
				outPt.Next.Prev = result;
				outPt.Next = result;
			}
			else
			{
				result.Prev = outPt.Prev;
				result.Next = outPt;
				outPt.Prev.Next = result;
				outPt.Prev = result;
			}
			return result;
		}
		//------------------------------------------------------------------------------

		bool GetOverlap(cInt a1, cInt a2, cInt b1, cInt b2, out cInt Left, out cInt Right)
		{
			if (a1 < a2)
			{
				if (b1 < b2) { Left = Math.Max(a1, b1); Right = Math.Min(a2, b2); }
				else { Left = Math.Max(a1, b2); Right = Math.Min(a2, b1); }
			}
			else
			{
				if (b1 < b2) { Left = Math.Max(a2, b1); Right = Math.Min(a1, b2); }
				else { Left = Math.Max(a2, b2); Right = Math.Min(a1, b1); }
			}
			return Left < Right;
		}
		//------------------------------------------------------------------------------

		bool JoinHorz(OutPt op1, OutPt op1b, OutPt op2, OutPt op2b,
		  IntPoint Pt, bool DiscardLeft)
		{
			Direction Dir1 = (op1.Pt.X > op1b.Pt.X ?
			  Direction.dRightToLeft : Direction.dLeftToRight);
			Direction Dir2 = (op2.Pt.X > op2b.Pt.X ?
			  Direction.dRightToLeft : Direction.dLeftToRight);
			if (Dir1 == Dir2) return false;

			//When DiscardLeft, we want Op1b to be on the Left of Op1, otherwise we
			//want Op1b to be on the Right. (And likewise with Op2 and Op2b.)
			//So, to facilitate this while inserting Op1b and Op2b ...
			//when DiscardLeft, make sure we're AT or RIGHT of Pt before adding Op1b,
			//otherwise make sure we're AT or LEFT of Pt. (Likewise with Op2b.)
			if (Dir1 == Direction.dLeftToRight)
			{
				while (op1.Next.Pt.X <= Pt.X &&
				  op1.Next.Pt.X >= op1.Pt.X && op1.Next.Pt.Y == Pt.Y)
					op1 = op1.Next;
				if (DiscardLeft && (op1.Pt.X != Pt.X)) op1 = op1.Next;
				op1b = DupOutPt(op1, !DiscardLeft);
				if (op1b.Pt != Pt)
				{
					op1 = op1b;
					op1.Pt = Pt;
					op1b = DupOutPt(op1, !DiscardLeft);
				}
			}
			else
			{
				while (op1.Next.Pt.X >= Pt.X &&
				  op1.Next.Pt.X <= op1.Pt.X && op1.Next.Pt.Y == Pt.Y)
					op1 = op1.Next;
				if (!DiscardLeft && (op1.Pt.X != Pt.X)) op1 = op1.Next;
				op1b = DupOutPt(op1, DiscardLeft);
				if (op1b.Pt != Pt)
				{
					op1 = op1b;
					op1.Pt = Pt;
					op1b = DupOutPt(op1, DiscardLeft);
				}
			}

			if (Dir2 == Direction.dLeftToRight)
			{
				while (op2.Next.Pt.X <= Pt.X &&
				  op2.Next.Pt.X >= op2.Pt.X && op2.Next.Pt.Y == Pt.Y)
					op2 = op2.Next;
				if (DiscardLeft && (op2.Pt.X != Pt.X)) op2 = op2.Next;
				op2b = DupOutPt(op2, !DiscardLeft);
				if (op2b.Pt != Pt)
				{
					op2 = op2b;
					op2.Pt = Pt;
					op2b = DupOutPt(op2, !DiscardLeft);
				};
			}
			else
			{
				while (op2.Next.Pt.X >= Pt.X &&
				  op2.Next.Pt.X <= op2.Pt.X && op2.Next.Pt.Y == Pt.Y)
					op2 = op2.Next;
				if (!DiscardLeft && (op2.Pt.X != Pt.X)) op2 = op2.Next;
				op2b = DupOutPt(op2, DiscardLeft);
				if (op2b.Pt != Pt)
				{
					op2 = op2b;
					op2.Pt = Pt;
					op2b = DupOutPt(op2, DiscardLeft);
				};
			};

			if ((Dir1 == Direction.dLeftToRight) == DiscardLeft)
			{
				op1.Prev = op2;
				op2.Next = op1;
				op1b.Next = op2b;
				op2b.Prev = op1b;
			}
			else
			{
				op1.Next = op2;
				op2.Prev = op1;
				op1b.Prev = op2b;
				op2b.Next = op1b;
			}
			return true;
		}
		//------------------------------------------------------------------------------

		private bool JoinPoints(Join j, OutRec outRec1, OutRec outRec2)
		{
			OutPt op1 = j.OutPt1, op1b;
			OutPt op2 = j.OutPt2, op2b;

			//There are 3 kinds of joins for output polygons ...
			//1. Horizontal joins where Join.OutPt1 & Join.OutPt2 are vertices anywhere
			//along (horizontal) collinear edges (& Join.OffPt is on the same horizontal).
			//2. Non-horizontal joins where Join.OutPt1 & Join.OutPt2 are at the same
			//location at the Bottom of the overlapping segment (& Join.OffPt is above).
			//3. StrictlySimple joins where edges touch but are not collinear and where
			//Join.OutPt1, Join.OutPt2 & Join.OffPt all share the same point.
			bool isHorizontal = (j.OutPt1.Pt.Y == j.OffPt.Y);

			if (isHorizontal && (j.OffPt == j.OutPt1.Pt) && (j.OffPt == j.OutPt2.Pt))
			{
				//Strictly Simple join ...
				if (outRec1 != outRec2) return false;
				op1b = j.OutPt1.Next;
				while (op1b != op1 && (op1b.Pt == j.OffPt))
					op1b = op1b.Next;
				bool reverse1 = (op1b.Pt.Y > j.OffPt.Y);
				op2b = j.OutPt2.Next;
				while (op2b != op2 && (op2b.Pt == j.OffPt))
					op2b = op2b.Next;
				bool reverse2 = (op2b.Pt.Y > j.OffPt.Y);
				if (reverse1 == reverse2) return false;
				if (reverse1)
				{
					op1b = DupOutPt(op1, false);
					op2b = DupOutPt(op2, true);
					op1.Prev = op2;
					op2.Next = op1;
					op1b.Next = op2b;
					op2b.Prev = op1b;
					j.OutPt1 = op1;
					j.OutPt2 = op1b;
					return true;
				}
				else
				{
					op1b = DupOutPt(op1, true);
					op2b = DupOutPt(op2, false);
					op1.Next = op2;
					op2.Prev = op1;
					op1b.Prev = op2b;
					op2b.Next = op1b;
					j.OutPt1 = op1;
					j.OutPt2 = op1b;
					return true;
				}
			}
			else if (isHorizontal)
			{
				//treat horizontal joins differently to non-horizontal joins since with
				//them we're not yet sure where the overlapping is. OutPt1.Pt & OutPt2.Pt
				//may be anywhere along the horizontal edge.
				op1b = op1;
				while (op1.Prev.Pt.Y == op1.Pt.Y && op1.Prev != op1b && op1.Prev != op2)
					op1 = op1.Prev;
				while (op1b.Next.Pt.Y == op1b.Pt.Y && op1b.Next != op1 && op1b.Next != op2)
					op1b = op1b.Next;
				if (op1b.Next == op1 || op1b.Next == op2) return false; //a flat 'polygon'

				op2b = op2;
				while (op2.Prev.Pt.Y == op2.Pt.Y && op2.Prev != op2b && op2.Prev != op1b)
					op2 = op2.Prev;
				while (op2b.Next.Pt.Y == op2b.Pt.Y && op2b.Next != op2 && op2b.Next != op1)
					op2b = op2b.Next;
				if (op2b.Next == op2 || op2b.Next == op1) return false; //a flat 'polygon'

				cInt Left, Right;
				//Op1 -. Op1b & Op2 -. Op2b are the extremites of the horizontal edges
				if (!GetOverlap(op1.Pt.X, op1b.Pt.X, op2.Pt.X, op2b.Pt.X, out Left, out Right))
					return false;

				//DiscardLeftSide: when overlapping edges are joined, a spike will created
				//which needs to be cleaned up. However, we don't want Op1 or Op2 caught up
				//on the discard Side as either may still be needed for other joins ...
				IntPoint Pt;
				bool DiscardLeftSide;
				if (op1.Pt.X >= Left && op1.Pt.X <= Right)
				{
					Pt = op1.Pt; DiscardLeftSide = (op1.Pt.X > op1b.Pt.X);
				}
				else if (op2.Pt.X >= Left && op2.Pt.X <= Right)
				{
					Pt = op2.Pt; DiscardLeftSide = (op2.Pt.X > op2b.Pt.X);
				}
				else if (op1b.Pt.X >= Left && op1b.Pt.X <= Right)
				{
					Pt = op1b.Pt; DiscardLeftSide = op1b.Pt.X > op1.Pt.X;
				}
				else
				{
					Pt = op2b.Pt; DiscardLeftSide = (op2b.Pt.X > op2.Pt.X);
				}
				j.OutPt1 = op1;
				j.OutPt2 = op2;
				return JoinHorz(op1, op1b, op2, op2b, Pt, DiscardLeftSide);
			}
			else
			{
				//nb: For non-horizontal joins ...
				//    1. Jr.OutPt1.Pt.Y == Jr.OutPt2.Pt.Y
				//    2. Jr.OutPt1.Pt > Jr.OffPt.Y

				//make sure the polygons are correctly oriented ...
				op1b = op1.Next;
				while ((op1b.Pt == op1.Pt) && (op1b != op1)) op1b = op1b.Next;
				bool Reverse1 = ((op1b.Pt.Y > op1.Pt.Y) ||
				  !SlopesEqual(op1.Pt, op1b.Pt, j.OffPt, m_UseFullRange));
				if (Reverse1)
				{
					op1b = op1.Prev;
					while ((op1b.Pt == op1.Pt) && (op1b != op1)) op1b = op1b.Prev;
					if ((op1b.Pt.Y > op1.Pt.Y) ||
					  !SlopesEqual(op1.Pt, op1b.Pt, j.OffPt, m_UseFullRange)) return false;
				};
				op2b = op2.Next;
				while ((op2b.Pt == op2.Pt) && (op2b != op2)) op2b = op2b.Next;
				bool Reverse2 = ((op2b.Pt.Y > op2.Pt.Y) ||
				  !SlopesEqual(op2.Pt, op2b.Pt, j.OffPt, m_UseFullRange));
				if (Reverse2)
				{
					op2b = op2.Prev;
					while ((op2b.Pt == op2.Pt) && (op2b != op2)) op2b = op2b.Prev;
					if ((op2b.Pt.Y > op2.Pt.Y) ||
					  !SlopesEqual(op2.Pt, op2b.Pt, j.OffPt, m_UseFullRange)) return false;
				}

				if ((op1b == op1) || (op2b == op2) || (op1b == op2b) ||
				  ((outRec1 == outRec2) && (Reverse1 == Reverse2))) return false;

				if (Reverse1)
				{
					op1b = DupOutPt(op1, false);
					op2b = DupOutPt(op2, true);
					op1.Prev = op2;
					op2.Next = op1;
					op1b.Next = op2b;
					op2b.Prev = op1b;
					j.OutPt1 = op1;
					j.OutPt2 = op1b;
					return true;
				}
				else
				{
					op1b = DupOutPt(op1, true);
					op2b = DupOutPt(op2, false);
					op1.Next = op2;
					op2.Prev = op1;
					op1b.Prev = op2b;
					op2b.Next = op1b;
					j.OutPt1 = op1;
					j.OutPt2 = op1b;
					return true;
				}
			}
		}
		//----------------------------------------------------------------------

		public static int PointInPolygon(IntPoint pt, Path path)
		{
			//returns 0 if false, +1 if true, -1 if pt ON polygon boundary
			//See "The Point in Polygon Problem for Arbitrary Polygons" by Hormann & Agathos
			//http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.88.5498&rep=rep1&type=pdf
			int result = 0, cnt = path.Count;
			if (cnt < 3) return 0;
			IntPoint ip = path[0];
			for (int i = 1; i <= cnt; ++i)
			{
				IntPoint ipNext = (i == cnt ? path[0] : path[i]);
				if (ipNext.Y == pt.Y)
				{
					if ((ipNext.X == pt.X) || (ip.Y == pt.Y &&
					  ((ipNext.X > pt.X) == (ip.X < pt.X)))) return -1;
				}
				if ((ip.Y < pt.Y) != (ipNext.Y < pt.Y))
				{
					if (ip.X >= pt.X)
					{
						if (ipNext.X > pt.X) result = 1 - result;
						else
						{
							double d = (double)(ip.X - pt.X) * (ipNext.Y - pt.Y) -
							  (double)(ipNext.X - pt.X) * (ip.Y - pt.Y);
							if (d == 0) return -1;
							else if ((d > 0) == (ipNext.Y > ip.Y)) result = 1 - result;
						}
					}
					else
					{
						if (ipNext.X > pt.X)
						{
							double d = (double)(ip.X - pt.X) * (ipNext.Y - pt.Y) -
							  (double)(ipNext.X - pt.X) * (ip.Y - pt.Y);
							if (d == 0) return -1;
							else if ((d > 0) == (ipNext.Y > ip.Y)) result = 1 - result;
						}
					}
				}
				ip = ipNext;
			}
			return result;
		}
		//------------------------------------------------------------------------------

		//See "The Point in Polygon Problem for Arbitrary Polygons" by Hormann & Agathos
		//http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.88.5498&rep=rep1&type=pdf
		private static int PointInPolygon(IntPoint pt, OutPt op)
		{
			//returns 0 if false, +1 if true, -1 if pt ON polygon boundary
			int result = 0;
			OutPt startOp = op;
			cInt ptx = pt.X, pty = pt.Y;
			cInt poly0x = op.Pt.X, poly0y = op.Pt.Y;
			do
			{
				op = op.Next;
				cInt poly1x = op.Pt.X, poly1y = op.Pt.Y;

				if (poly1y == pty)
				{
					if ((poly1x == ptx) || (poly0y == pty &&
					  ((poly1x > ptx) == (poly0x < ptx)))) return -1;
				}
				if ((poly0y < pty) != (poly1y < pty))
				{
					if (poly0x >= ptx)
					{
						if (poly1x > ptx) result = 1 - result;
						else
						{
							double d = (double)(poly0x - ptx) * (poly1y - pty) -
							  (double)(poly1x - ptx) * (poly0y - pty);
							if (d == 0) return -1;
							if ((d > 0) == (poly1y > poly0y)) result = 1 - result;
						}
					}
					else
					{
						if (poly1x > ptx)
						{
							double d = (double)(poly0x - ptx) * (poly1y - pty) -
							  (double)(poly1x - ptx) * (poly0y - pty);
							if (d == 0) return -1;
							if ((d > 0) == (poly1y > poly0y)) result = 1 - result;
						}
					}
				}
				poly0x = poly1x; poly0y = poly1y;
			} while (startOp != op);
			return result;
		}
		//------------------------------------------------------------------------------

		private static bool Poly2ContainsPoly1(OutPt outPt1, OutPt outPt2)
		{
			OutPt op = outPt1;
			do
			{
				//nb: PointInPolygon returns 0 if false, +1 if true, -1 if pt on polygon
				int res = PointInPolygon(op.Pt, outPt2);
				if (res >= 0) return res > 0;
				op = op.Next;
			}
			while (op != outPt1);
			return true;
		}
		//----------------------------------------------------------------------

		private void FixupFirstLefts1(OutRec OldOutRec, OutRec NewOutRec)
		{
			foreach (OutRec outRec in m_PolyOuts)
			{
				OutRec firstLeft = ParseFirstLeft(outRec.FirstLeft);
				if (outRec.Pts != null && firstLeft == OldOutRec)
				{
					if (Poly2ContainsPoly1(outRec.Pts, NewOutRec.Pts))
						outRec.FirstLeft = NewOutRec;
				}
			}
		}
		//----------------------------------------------------------------------

		private void FixupFirstLefts2(OutRec innerOutRec, OutRec outerOutRec)
		{
			//A polygon has split into two such that one is now the inner of the other.
			//It's possible that these polygons now wrap around other polygons, so check
			//every polygon that's also contained by OuterOutRec's FirstLeft container
			//(including nil) to see if they've become inner to the new inner polygon ...
			OutRec orfl = outerOutRec.FirstLeft;
			foreach (OutRec outRec in m_PolyOuts)
			{
				if (outRec.Pts == null || outRec == outerOutRec || outRec == innerOutRec)
					continue;
				OutRec firstLeft = ParseFirstLeft(outRec.FirstLeft);
				if (firstLeft != orfl && firstLeft != innerOutRec && firstLeft != outerOutRec)
					continue;
				if (Poly2ContainsPoly1(outRec.Pts, innerOutRec.Pts))
					outRec.FirstLeft = innerOutRec;
				else if (Poly2ContainsPoly1(outRec.Pts, outerOutRec.Pts))
					outRec.FirstLeft = outerOutRec;
				else if (outRec.FirstLeft == innerOutRec || outRec.FirstLeft == outerOutRec)
					outRec.FirstLeft = orfl;
			}
		}
		//----------------------------------------------------------------------

		private void FixupFirstLefts3(OutRec OldOutRec, OutRec NewOutRec)
		{
			//same as FixupFirstLefts1 but doesn't call Poly2ContainsPoly1()
			foreach (OutRec outRec in m_PolyOuts)
			{
				OutRec firstLeft = ParseFirstLeft(outRec.FirstLeft);
				if (outRec.Pts != null && firstLeft == OldOutRec)
					outRec.FirstLeft = NewOutRec;
			}
		}
		//----------------------------------------------------------------------

		private static OutRec ParseFirstLeft(OutRec FirstLeft)
		{
			while (FirstLeft != null && FirstLeft.Pts == null)
				FirstLeft = FirstLeft.FirstLeft;
			return FirstLeft;
		}
		//------------------------------------------------------------------------------

		private void JoinCommonEdges()
		{
			for (int i = 0; i < m_Joins.Count; i++)
			{
				Join join = m_Joins[i];

				OutRec outRec1 = GetOutRec(join.OutPt1.Idx);
				OutRec outRec2 = GetOutRec(join.OutPt2.Idx);

				if (outRec1.Pts == null || outRec2.Pts == null) continue;
				if (outRec1.IsOpen || outRec2.IsOpen) continue;

				//get the polygon fragment with the correct hole state (FirstLeft)
				//before calling JoinPoints() ...
				OutRec holeStateRec;
				if (outRec1 == outRec2) holeStateRec = outRec1;
				else if (OutRec1RightOfOutRec2(outRec1, outRec2)) holeStateRec = outRec2;
				else if (OutRec1RightOfOutRec2(outRec2, outRec1)) holeStateRec = outRec1;
				else holeStateRec = GetLowermostRec(outRec1, outRec2);

				if (!JoinPoints(join, outRec1, outRec2)) continue;

				if (outRec1 == outRec2)
				{
					//instead of joining two polygons, we've just created a new one by
					//splitting one polygon into two.
					outRec1.Pts = join.OutPt1;
					outRec1.BottomPt = null;
					outRec2 = CreateOutRec();
					outRec2.Pts = join.OutPt2;

					//update all OutRec2.Pts Idx's ...
					UpdateOutPtIdxs(outRec2);

					if (Poly2ContainsPoly1(outRec2.Pts, outRec1.Pts))
					{
						//outRec1 contains outRec2 ...
						outRec2.IsHole = !outRec1.IsHole;
						outRec2.FirstLeft = outRec1;

						if (m_UsingPolyTree) FixupFirstLefts2(outRec2, outRec1);

						if ((outRec2.IsHole ^ ReverseSolution) == (Area(outRec2) > 0))
							ReversePolyPtLinks(outRec2.Pts);

					}
					else if (Poly2ContainsPoly1(outRec1.Pts, outRec2.Pts))
					{
						//outRec2 contains outRec1 ...
						outRec2.IsHole = outRec1.IsHole;
						outRec1.IsHole = !outRec2.IsHole;
						outRec2.FirstLeft = outRec1.FirstLeft;
						outRec1.FirstLeft = outRec2;

						if (m_UsingPolyTree) FixupFirstLefts2(outRec1, outRec2);

						if ((outRec1.IsHole ^ ReverseSolution) == (Area(outRec1) > 0))
							ReversePolyPtLinks(outRec1.Pts);
					}
					else
					{
						//the 2 polygons are completely separate ...
						outRec2.IsHole = outRec1.IsHole;
						outRec2.FirstLeft = outRec1.FirstLeft;

						//fixup FirstLeft pointers that may need reassigning to OutRec2
						if (m_UsingPolyTree) FixupFirstLefts1(outRec1, outRec2);
					}

				}
				else
				{
					//joined 2 polygons together ...

					outRec2.Pts = null;
					outRec2.BottomPt = null;
					outRec2.Idx = outRec1.Idx;

					outRec1.IsHole = holeStateRec.IsHole;
					if (holeStateRec == outRec2)
						outRec1.FirstLeft = outRec2.FirstLeft;
					outRec2.FirstLeft = outRec1;

					//fixup FirstLeft pointers that may need reassigning to OutRec1
					if (m_UsingPolyTree) FixupFirstLefts3(outRec2, outRec1);
				}
			}
		}
		//------------------------------------------------------------------------------

		private void UpdateOutPtIdxs(OutRec outrec)
		{
			OutPt op = outrec.Pts;
			do
			{
				op.Idx = outrec.Idx;
				op = op.Prev;
			}
			while (op != outrec.Pts);
		}
		//------------------------------------------------------------------------------

		private void DoSimplePolygons()
		{
			int i = 0;
			while (i < m_PolyOuts.Count)
			{
				OutRec outrec = m_PolyOuts[i++];
				OutPt op = outrec.Pts;
				if (op == null || outrec.IsOpen) continue;
				do //for each Pt in Polygon until duplicate found do ...
				{
					OutPt op2 = op.Next;
					while (op2 != outrec.Pts)
					{
						if ((op.Pt == op2.Pt) && op2.Next != op && op2.Prev != op)
						{
							//split the polygon into two ...
							OutPt op3 = op.Prev;
							OutPt op4 = op2.Prev;
							op.Prev = op4;
							op4.Next = op;
							op2.Prev = op3;
							op3.Next = op2;

							outrec.Pts = op;
							OutRec outrec2 = CreateOutRec();
							outrec2.Pts = op2;
							UpdateOutPtIdxs(outrec2);
							if (Poly2ContainsPoly1(outrec2.Pts, outrec.Pts))
							{
								//OutRec2 is contained by OutRec1 ...
								outrec2.IsHole = !outrec.IsHole;
								outrec2.FirstLeft = outrec;
								if (m_UsingPolyTree) FixupFirstLefts2(outrec2, outrec);
							}
							else
							if (Poly2ContainsPoly1(outrec.Pts, outrec2.Pts))
							{
								//OutRec1 is contained by OutRec2 ...
								outrec2.IsHole = outrec.IsHole;
								outrec.IsHole = !outrec2.IsHole;
								outrec2.FirstLeft = outrec.FirstLeft;
								outrec.FirstLeft = outrec2;
								if (m_UsingPolyTree) FixupFirstLefts2(outrec, outrec2);
							}
							else
							{
								//the 2 polygons are separate ...
								outrec2.IsHole = outrec.IsHole;
								outrec2.FirstLeft = outrec.FirstLeft;
								if (m_UsingPolyTree) FixupFirstLefts1(outrec, outrec2);
							}
							op2 = op; //ie get ready for the next iteration
						}
						op2 = op2.Next;
					}
					op = op.Next;
				}
				while (op != outrec.Pts);
			}
		}
		//------------------------------------------------------------------------------

		public static double Area(Path poly)
		{
			int cnt = (int)poly.Count;
			if (cnt < 3) return 0;
			double a = 0;
			for (int i = 0, j = cnt - 1; i < cnt; ++i)
			{
				a += ((double)poly[j].X + poly[i].X) * ((double)poly[j].Y - poly[i].Y);
				j = i;
			}
			return -a * 0.5;
		}
		//------------------------------------------------------------------------------

		internal double Area(OutRec outRec)
		{
			return Area(outRec.Pts);
		}
		//------------------------------------------------------------------------------

		internal double Area(OutPt op)
		{
			OutPt opFirst = op;
			if (op == null) return 0;
			double a = 0;
			do
			{
				a = a + (double)(op.Prev.Pt.X + op.Pt.X) * (double)(op.Prev.Pt.Y - op.Pt.Y);
				op = op.Next;
			} while (op != opFirst);
			return a * 0.5;
		}

		//------------------------------------------------------------------------------
		// SimplifyPolygon functions ...
		// Convert self-intersecting polygons into simple polygons
		//------------------------------------------------------------------------------

		public static Paths SimplifyPolygon(Path poly,
			  PolyFillType fillType = PolyFillType.pftEvenOdd)
		{
			Paths result = new Paths();
			Clipper c = new Clipper();
			c.StrictlySimple = true;
			c.AddPath(poly, PolyType.ptSubject, true);
			c.Execute(ClipType.ctUnion, result, fillType, fillType);
			return result;
		}
		//------------------------------------------------------------------------------

		public static Paths SimplifyPolygons(Paths polys,
			PolyFillType fillType = PolyFillType.pftEvenOdd)
		{
			Paths result = new Paths();
			Clipper c = new Clipper();
			c.StrictlySimple = true;
			c.AddPaths(polys, PolyType.ptSubject, true);
			c.Execute(ClipType.ctUnion, result, fillType, fillType);
			return result;
		}
		//------------------------------------------------------------------------------

		private static double DistanceSqrd(IntPoint pt1, IntPoint pt2)
		{
			double dx = ((double)pt1.X - pt2.X);
			double dy = ((double)pt1.Y - pt2.Y);
			return (dx * dx + dy * dy);
		}
		//------------------------------------------------------------------------------

		private static double DistanceFromLineSqrd(IntPoint pt, IntPoint ln1, IntPoint ln2)
		{
			//The equation of a line in general form (Ax + By + C = 0)
			//given 2 points (x¹,y¹) & (x²,y²) is ...
			//(y¹ - y²)x + (x² - x¹)y + (y² - y¹)x¹ - (x² - x¹)y¹ = 0
			//A = (y¹ - y²); B = (x² - x¹); C = (y² - y¹)x¹ - (x² - x¹)y¹
			//perpendicular distance of point (x³,y³) = (Ax³ + By³ + C)/Sqrt(A² + B²)
			//see http://en.wikipedia.org/wiki/Perpendicular_distance
			double A = ln1.Y - ln2.Y;
			double B = ln2.X - ln1.X;
			double C = A * ln1.X + B * ln1.Y;
			C = A * pt.X + B * pt.Y - C;
			return (C * C) / (A * A + B * B);
		}
		//---------------------------------------------------------------------------

		private static bool SlopesNearCollinear(IntPoint pt1,
			IntPoint pt2, IntPoint pt3, double distSqrd)
		{
			//this function is more accurate when the point that's GEOMETRICALLY 
			//between the other 2 points is the one that's tested for distance.  
			//nb: with 'spikes', either pt1 or pt3 is geometrically between the other pts                    
			if (Math.Abs(pt1.X - pt2.X) > Math.Abs(pt1.Y - pt2.Y))
			{
				if ((pt1.X > pt2.X) == (pt1.X < pt3.X))
					return DistanceFromLineSqrd(pt1, pt2, pt3) < distSqrd;
				else if ((pt2.X > pt1.X) == (pt2.X < pt3.X))
					return DistanceFromLineSqrd(pt2, pt1, pt3) < distSqrd;
				else
					return DistanceFromLineSqrd(pt3, pt1, pt2) < distSqrd;
			}
			else
			{
				if ((pt1.Y > pt2.Y) == (pt1.Y < pt3.Y))
					return DistanceFromLineSqrd(pt1, pt2, pt3) < distSqrd;
				else if ((pt2.Y > pt1.Y) == (pt2.Y < pt3.Y))
					return DistanceFromLineSqrd(pt2, pt1, pt3) < distSqrd;
				else
					return DistanceFromLineSqrd(pt3, pt1, pt2) < distSqrd;
			}
		}
		//------------------------------------------------------------------------------

		private static bool PointsAreClose(IntPoint pt1, IntPoint pt2, double distSqrd)
		{
			double dx = (double)pt1.X - pt2.X;
			double dy = (double)pt1.Y - pt2.Y;
			return ((dx * dx) + (dy * dy) <= distSqrd);
		}
		//------------------------------------------------------------------------------

		private static OutPt ExcludeOp(OutPt op)
		{
			OutPt result = op.Prev;
			result.Next = op.Next;
			op.Next.Prev = result;
			result.Idx = 0;
			return result;
		}
		//------------------------------------------------------------------------------

		public static Path CleanPolygon(Path path, double distance = 1.415)
		{
			//distance = proximity in units/pixels below which vertices will be stripped. 
			//Default ~= sqrt(2) so when adjacent vertices or semi-adjacent vertices have 
			//both x & y coords within 1 unit, then the second vertex will be stripped.

			int cnt = path.Count;

			if (cnt == 0) return new Path();

			OutPt[] outPts = new OutPt[cnt];
			for (int i = 0; i < cnt; ++i) outPts[i] = new OutPt();

			for (int i = 0; i < cnt; ++i)
			{
				outPts[i].Pt = path[i];
				outPts[i].Next = outPts[(i + 1) % cnt];
				outPts[i].Next.Prev = outPts[i];
				outPts[i].Idx = 0;
			}

			double distSqrd = distance * distance;
			OutPt op = outPts[0];
			while (op.Idx == 0 && op.Next != op.Prev)
			{
				if (PointsAreClose(op.Pt, op.Prev.Pt, distSqrd))
				{
					op = ExcludeOp(op);
					cnt--;
				}
				else if (PointsAreClose(op.Prev.Pt, op.Next.Pt, distSqrd))
				{
					ExcludeOp(op.Next);
					op = ExcludeOp(op);
					cnt -= 2;
				}
				else if (SlopesNearCollinear(op.Prev.Pt, op.Pt, op.Next.Pt, distSqrd))
				{
					op = ExcludeOp(op);
					cnt--;
				}
				else
				{
					op.Idx = 1;
					op = op.Next;
				}
			}

			if (cnt < 3) cnt = 0;
			Path result = new Path(cnt);
			for (int i = 0; i < cnt; ++i)
			{
				result.Add(op.Pt);
				op = op.Next;
			}
			outPts = null;
			return result;
		}
		//------------------------------------------------------------------------------

		public static Paths CleanPolygons(Paths polys,
			double distance = 1.415)
		{
			Paths result = new Paths(polys.Count);
			for (int i = 0; i < polys.Count; i++)
				result.Add(CleanPolygon(polys[i], distance));
			return result;
		}
		//------------------------------------------------------------------------------

		internal static Paths Minkowski(Path pattern, Path path, bool IsSum, bool IsClosed)
		{
			int delta = (IsClosed ? 1 : 0);
			int polyCnt = pattern.Count;
			int pathCnt = path.Count;
			Paths result = new Paths(pathCnt);
			if (IsSum)
				for (int i = 0; i < pathCnt; i++)
				{
					Path p = new Path(polyCnt);
					foreach (IntPoint ip in pattern)
						p.Add(new IntPoint(path[i].X + ip.X, path[i].Y + ip.Y));
					result.Add(p);
				}
			else
				for (int i = 0; i < pathCnt; i++)
				{
					Path p = new Path(polyCnt);
					foreach (IntPoint ip in pattern)
						p.Add(new IntPoint(path[i].X - ip.X, path[i].Y - ip.Y));
					result.Add(p);
				}

			Paths quads = new Paths((pathCnt + delta) * (polyCnt + 1));
			for (int i = 0; i < pathCnt - 1 + delta; i++)
				for (int j = 0; j < polyCnt; j++)
				{
					Path quad = new Path(4);
					quad.Add(result[i % pathCnt][j % polyCnt]);
					quad.Add(result[(i + 1) % pathCnt][j % polyCnt]);
					quad.Add(result[(i + 1) % pathCnt][(j + 1) % polyCnt]);
					quad.Add(result[i % pathCnt][(j + 1) % polyCnt]);
					if (!Orientation(quad)) quad.Reverse();
					quads.Add(quad);
				}
			return quads;
		}
		//------------------------------------------------------------------------------

		public static Paths MinkowskiSum(Path pattern, Path path, bool pathIsClosed)
		{
			Paths paths = Minkowski(pattern, path, true, pathIsClosed);
			Clipper c = new Clipper();
			c.AddPaths(paths, PolyType.ptSubject, true);
			c.Execute(ClipType.ctUnion, paths, PolyFillType.pftNonZero, PolyFillType.pftNonZero);
			return paths;
		}
		//------------------------------------------------------------------------------

		private static Path TranslatePath(Path path, IntPoint delta)
		{
			Path outPath = new Path(path.Count);
			for (int i = 0; i < path.Count; i++)
				outPath.Add(new IntPoint(path[i].X + delta.X, path[i].Y + delta.Y));
			return outPath;
		}
		//------------------------------------------------------------------------------

		public static Paths MinkowskiSum(Path pattern, Paths paths, bool pathIsClosed)
		{
			Paths solution = new Paths();
			Clipper c = new Clipper();
			for (int i = 0; i < paths.Count; ++i)
			{
				Paths tmp = Minkowski(pattern, paths[i], true, pathIsClosed);
				c.AddPaths(tmp, PolyType.ptSubject, true);
				if (pathIsClosed)
				{
					Path path = TranslatePath(paths[i], pattern[0]);
					c.AddPath(path, PolyType.ptClip, true);
				}
			}
			c.Execute(ClipType.ctUnion, solution,
			  PolyFillType.pftNonZero, PolyFillType.pftNonZero);
			return solution;
		}
		//------------------------------------------------------------------------------

		public static Paths MinkowskiDiff(Path poly1, Path poly2)
		{
			Paths paths = Minkowski(poly1, poly2, false, true);
			Clipper c = new Clipper();
			c.AddPaths(paths, PolyType.ptSubject, true);
			c.Execute(ClipType.ctUnion, paths, PolyFillType.pftNonZero, PolyFillType.pftNonZero);
			return paths;
		}
		//------------------------------------------------------------------------------

		internal enum NodeType { ntAny, ntOpen, ntClosed };

		public static Paths PolyTreeToPaths(PolyTree polytree)
		{

			Paths result = new Paths();
			result.Capacity = polytree.Total;
			AddPolyNodeToPaths(polytree, NodeType.ntAny, result);
			return result;
		}
		//------------------------------------------------------------------------------

		internal static void AddPolyNodeToPaths(PolyNode polynode, NodeType nt, Paths paths)
		{
			bool match = true;
			switch (nt)
			{
				case NodeType.ntOpen: return;
				case NodeType.ntClosed: match = !polynode.IsOpen; break;
				default: break;
			}

			if (polynode.m_polygon.Count > 0 && match)
				paths.Add(polynode.m_polygon);
			foreach (PolyNode pn in polynode.Childs)
				AddPolyNodeToPaths(pn, nt, paths);
		}
		//------------------------------------------------------------------------------

		public static Paths OpenPathsFromPolyTree(PolyTree polytree)
		{
			Paths result = new Paths();
			result.Capacity = polytree.ChildCount;
			for (int i = 0; i < polytree.ChildCount; i++)
				if (polytree.Childs[i].IsOpen)
					result.Add(polytree.Childs[i].m_polygon);
			return result;
		}
		//------------------------------------------------------------------------------

		public static Paths ClosedPathsFromPolyTree(PolyTree polytree)
		{
			Paths result = new Paths();
			result.Capacity = polytree.Total;
			AddPolyNodeToPaths(polytree, NodeType.ntClosed, result);
			return result;
		}
		//------------------------------------------------------------------------------

	} //end Clipper

	public class ClipperOffset
	{
		private Paths m_destPolys;
		private Path m_srcPoly;
		private Path m_destPoly;
		private List<DoublePoint> m_normals = new List<DoublePoint>();
		private double m_delta, m_sinA, m_sin, m_cos;
		private double m_miterLim, m_StepsPerRad;

		private IntPoint m_lowest;
		private PolyNode m_polyNodes = new PolyNode();

		public double ArcTolerance { get; set; }
		public double MiterLimit { get; set; }

		private const double two_pi = Math.PI * 2;
		private const double def_arc_tolerance = 0.25;

		public ClipperOffset(
		  double miterLimit = 2.0, double arcTolerance = def_arc_tolerance)
		{
			MiterLimit = miterLimit;
			ArcTolerance = arcTolerance;
			m_lowest.X = -1;
		}
		//------------------------------------------------------------------------------

		public void Clear()
		{
			m_polyNodes.Childs.Clear();
			m_lowest.X = -1;
		}
		//------------------------------------------------------------------------------

		internal static cInt Round(double value)
		{
			return value < 0 ? (cInt)(value - 0.5) : (cInt)(value + 0.5);
		}
		//------------------------------------------------------------------------------

		public void AddPath(Path path, JoinType joinType, EndType endType)
		{
			int highI = path.Count - 1;
			if (highI < 0) return;
			PolyNode newNode = new PolyNode();
			newNode.m_jointype = joinType;
			newNode.m_endtype = endType;

			//strip duplicate points from path and also get index to the lowest point ...
			if (endType == EndType.etClosedLine || endType == EndType.etClosedPolygon)
				while (highI > 0 && path[0] == path[highI]) highI--;
			newNode.m_polygon.Capacity = highI + 1;
			newNode.m_polygon.Add(path[0]);
			int j = 0, k = 0;
			for (int i = 1; i <= highI; i++)
				if (newNode.m_polygon[j] != path[i])
				{
					j++;
					newNode.m_polygon.Add(path[i]);
					if (path[i].Y > newNode.m_polygon[k].Y ||
					  (path[i].Y == newNode.m_polygon[k].Y &&
					  path[i].X < newNode.m_polygon[k].X)) k = j;
				}
			if (endType == EndType.etClosedPolygon && j < 2) return;

			m_polyNodes.AddChild(newNode);

			//if this path's lowest pt is lower than all the others then update m_lowest
			if (endType != EndType.etClosedPolygon) return;
			if (m_lowest.X < 0)
				m_lowest = new IntPoint(m_polyNodes.ChildCount - 1, k);
			else
			{
				IntPoint ip = m_polyNodes.Childs[(int)m_lowest.X].m_polygon[(int)m_lowest.Y];
				if (newNode.m_polygon[k].Y > ip.Y ||
				  (newNode.m_polygon[k].Y == ip.Y &&
				  newNode.m_polygon[k].X < ip.X))
					m_lowest = new IntPoint(m_polyNodes.ChildCount - 1, k);
			}
		}
		//------------------------------------------------------------------------------

		public void AddPaths(Paths paths, JoinType joinType, EndType endType)
		{
			foreach (Path p in paths)
				AddPath(p, joinType, endType);
		}
		//------------------------------------------------------------------------------

		private void FixOrientations()
		{
			//fixup orientations of all closed paths if the orientation of the
			//closed path with the lowermost vertex is wrong ...
			if (m_lowest.X >= 0 &&
			  !Clipper.Orientation(m_polyNodes.Childs[(int)m_lowest.X].m_polygon))
			{
				for (int i = 0; i < m_polyNodes.ChildCount; i++)
				{
					PolyNode node = m_polyNodes.Childs[i];
					if (node.m_endtype == EndType.etClosedPolygon ||
					  (node.m_endtype == EndType.etClosedLine &&
					  Clipper.Orientation(node.m_polygon)))
						node.m_polygon.Reverse();
				}
			}
			else
			{
				for (int i = 0; i < m_polyNodes.ChildCount; i++)
				{
					PolyNode node = m_polyNodes.Childs[i];
					if (node.m_endtype == EndType.etClosedLine &&
					  !Clipper.Orientation(node.m_polygon))
						node.m_polygon.Reverse();
				}
			}
		}
		//------------------------------------------------------------------------------

		internal static DoublePoint GetUnitNormal(IntPoint pt1, IntPoint pt2)
		{
			double dx = (pt2.X - pt1.X);
			double dy = (pt2.Y - pt1.Y);
			if ((dx == 0) && (dy == 0)) return new DoublePoint();

			double f = 1 * 1.0 / Math.Sqrt(dx * dx + dy * dy);
			dx *= f;
			dy *= f;

			return new DoublePoint(dy, -dx);
		}
		//------------------------------------------------------------------------------

		private void DoOffset(double delta)
		{
			m_destPolys = new Paths();
			m_delta = delta;

			//if Zero offset, just copy any CLOSED polygons to m_p and return ...
			if (ClipperBase.near_zero(delta))
			{
				m_destPolys.Capacity = m_polyNodes.ChildCount;
				for (int i = 0; i < m_polyNodes.ChildCount; i++)
				{
					PolyNode node = m_polyNodes.Childs[i];
					if (node.m_endtype == EndType.etClosedPolygon)
						m_destPolys.Add(node.m_polygon);
				}
				return;
			}

			//see offset_triginometry3.svg in the documentation folder ...
			if (MiterLimit > 2) m_miterLim = 2 / (MiterLimit * MiterLimit);
			else m_miterLim = 0.5;

			double y;
			if (ArcTolerance <= 0.0)
				y = def_arc_tolerance;
			else if (ArcTolerance > Math.Abs(delta) * def_arc_tolerance)
				y = Math.Abs(delta) * def_arc_tolerance;
			else
				y = ArcTolerance;
			//see offset_triginometry2.svg in the documentation folder ...
			double steps = Math.PI / Math.Acos(1 - y / Math.Abs(delta));
			m_sin = Math.Sin(two_pi / steps);
			m_cos = Math.Cos(two_pi / steps);
			m_StepsPerRad = steps / two_pi;
			if (delta < 0.0) m_sin = -m_sin;

			m_destPolys.Capacity = m_polyNodes.ChildCount * 2;
			for (int i = 0; i < m_polyNodes.ChildCount; i++)
			{
				PolyNode node = m_polyNodes.Childs[i];
				m_srcPoly = node.m_polygon;

				int len = m_srcPoly.Count;

				if (len == 0 || (delta <= 0 && (len < 3 ||
				  node.m_endtype != EndType.etClosedPolygon)))
					continue;

				m_destPoly = new Path();

				if (len == 1)
				{
					if (node.m_jointype == JoinType.jtRound)
					{
						double X = 1.0, Y = 0.0;
						for (int j = 1; j <= steps; j++)
						{
							m_destPoly.Add(new IntPoint(
							  Round(m_srcPoly[0].X + X * delta),
							  Round(m_srcPoly[0].Y + Y * delta)));
							double X2 = X;
							X = X * m_cos - m_sin * Y;
							Y = X2 * m_sin + Y * m_cos;
						}
					}
					else
					{
						double X = -1.0, Y = -1.0;
						for (int j = 0; j < 4; ++j)
						{
							m_destPoly.Add(new IntPoint(
							  Round(m_srcPoly[0].X + X * delta),
							  Round(m_srcPoly[0].Y + Y * delta)));
							if (X < 0) X = 1;
							else if (Y < 0) Y = 1;
							else X = -1;
						}
					}
					m_destPolys.Add(m_destPoly);
					continue;
				}

				//build m_normals ...
				m_normals.Clear();
				m_normals.Capacity = len;
				for (int j = 0; j < len - 1; j++)
					m_normals.Add(GetUnitNormal(m_srcPoly[j], m_srcPoly[j + 1]));
				if (node.m_endtype == EndType.etClosedLine ||
				  node.m_endtype == EndType.etClosedPolygon)
					m_normals.Add(GetUnitNormal(m_srcPoly[len - 1], m_srcPoly[0]));
				else
					m_normals.Add(new DoublePoint(m_normals[len - 2]));

				if (node.m_endtype == EndType.etClosedPolygon)
				{
					int k = len - 1;
					for (int j = 0; j < len; j++)
						OffsetPoint(j, ref k, node.m_jointype);
					m_destPolys.Add(m_destPoly);
				}
				else if (node.m_endtype == EndType.etClosedLine)
				{
					int k = len - 1;
					for (int j = 0; j < len; j++)
						OffsetPoint(j, ref k, node.m_jointype);
					m_destPolys.Add(m_destPoly);
					m_destPoly = new Path();
					//re-build m_normals ...
					DoublePoint n = m_normals[len - 1];
					for (int j = len - 1; j > 0; j--)
						m_normals[j] = new DoublePoint(-m_normals[j - 1].X, -m_normals[j - 1].Y);
					m_normals[0] = new DoublePoint(-n.X, -n.Y);
					k = 0;
					for (int j = len - 1; j >= 0; j--)
						OffsetPoint(j, ref k, node.m_jointype);
					m_destPolys.Add(m_destPoly);
				}
				else
				{
					int k = 0;
					for (int j = 1; j < len - 1; ++j)
						OffsetPoint(j, ref k, node.m_jointype);

					IntPoint pt1;
					if (node.m_endtype == EndType.etOpenButt)
					{
						int j = len - 1;
						pt1 = new IntPoint((cInt)Round(m_srcPoly[j].X + m_normals[j].X *
						  delta), (cInt)Round(m_srcPoly[j].Y + m_normals[j].Y * delta));
						m_destPoly.Add(pt1);
						pt1 = new IntPoint((cInt)Round(m_srcPoly[j].X - m_normals[j].X *
						  delta), (cInt)Round(m_srcPoly[j].Y - m_normals[j].Y * delta));
						m_destPoly.Add(pt1);
					}
					else
					{
						int j = len - 1;
						k = len - 2;
						m_sinA = 0;
						m_normals[j] = new DoublePoint(-m_normals[j].X, -m_normals[j].Y);
						if (node.m_endtype == EndType.etOpenSquare)
							DoSquare(j, k);
						else
							DoRound(j, k);
					}

					//re-build m_normals ...
					for (int j = len - 1; j > 0; j--)
						m_normals[j] = new DoublePoint(-m_normals[j - 1].X, -m_normals[j - 1].Y);

					m_normals[0] = new DoublePoint(-m_normals[1].X, -m_normals[1].Y);

					k = len - 1;
					for (int j = k - 1; j > 0; --j)
						OffsetPoint(j, ref k, node.m_jointype);

					if (node.m_endtype == EndType.etOpenButt)
					{
						pt1 = new IntPoint((cInt)Round(m_srcPoly[0].X - m_normals[0].X * delta),
						  (cInt)Round(m_srcPoly[0].Y - m_normals[0].Y * delta));
						m_destPoly.Add(pt1);
						pt1 = new IntPoint((cInt)Round(m_srcPoly[0].X + m_normals[0].X * delta),
						  (cInt)Round(m_srcPoly[0].Y + m_normals[0].Y * delta));
						m_destPoly.Add(pt1);
					}
					else
					{
						k = 1;
						m_sinA = 0;
						if (node.m_endtype == EndType.etOpenSquare)
							DoSquare(0, 1);
						else
							DoRound(0, 1);
					}
					m_destPolys.Add(m_destPoly);
				}
			}
		}
		//------------------------------------------------------------------------------

		public void Execute(ref Paths solution, double delta)
		{
			solution.Clear();
			FixOrientations();
			DoOffset(delta);
			//now clean up 'corners' ...
			Clipper clpr = new Clipper();
			clpr.AddPaths(m_destPolys, PolyType.ptSubject, true);
			if (delta > 0)
			{
				clpr.Execute(ClipType.ctUnion, solution,
				  PolyFillType.pftPositive, PolyFillType.pftPositive);
			}
			else
			{
				IntRect r = Clipper.GetBounds(m_destPolys);
				Path outer = new Path(4);

				outer.Add(new IntPoint(r.left - 10, r.bottom + 10));
				outer.Add(new IntPoint(r.right + 10, r.bottom + 10));
				outer.Add(new IntPoint(r.right + 10, r.top - 10));
				outer.Add(new IntPoint(r.left - 10, r.top - 10));

				clpr.AddPath(outer, PolyType.ptSubject, true);
				clpr.ReverseSolution = true;
				clpr.Execute(ClipType.ctUnion, solution, PolyFillType.pftNegative, PolyFillType.pftNegative);
				if (solution.Count > 0) solution.RemoveAt(0);
			}
		}
		//------------------------------------------------------------------------------

		public void Execute(ref PolyTree solution, double delta)
		{
			solution.Clear();
			FixOrientations();
			DoOffset(delta);

			//now clean up 'corners' ...
			Clipper clpr = new Clipper();
			clpr.AddPaths(m_destPolys, PolyType.ptSubject, true);
			if (delta > 0)
			{
				clpr.Execute(ClipType.ctUnion, solution,
				  PolyFillType.pftPositive, PolyFillType.pftPositive);
			}
			else
			{
				IntRect r = Clipper.GetBounds(m_destPolys);
				Path outer = new Path(4);

				outer.Add(new IntPoint(r.left - 10, r.bottom + 10));
				outer.Add(new IntPoint(r.right + 10, r.bottom + 10));
				outer.Add(new IntPoint(r.right + 10, r.top - 10));
				outer.Add(new IntPoint(r.left - 10, r.top - 10));

				clpr.AddPath(outer, PolyType.ptSubject, true);
				clpr.ReverseSolution = true;
				clpr.Execute(ClipType.ctUnion, solution, PolyFillType.pftNegative, PolyFillType.pftNegative);
				//remove the outer PolyNode rectangle ...
				if (solution.ChildCount == 1 && solution.Childs[0].ChildCount > 0)
				{
					PolyNode outerNode = solution.Childs[0];
					solution.Childs.Capacity = outerNode.ChildCount;
					solution.Childs[0] = outerNode.Childs[0];
					solution.Childs[0].m_Parent = solution;
					for (int i = 1; i < outerNode.ChildCount; i++)
						solution.AddChild(outerNode.Childs[i]);
				}
				else
					solution.Clear();
			}
		}
		//------------------------------------------------------------------------------

		void OffsetPoint(int j, ref int k, JoinType jointype)
		{
			//cross product ...
			m_sinA = (m_normals[k].X * m_normals[j].Y - m_normals[j].X * m_normals[k].Y);

			if (Math.Abs(m_sinA * m_delta) < 1.0)
			{
				//dot product ...
				double cosA = (m_normals[k].X * m_normals[j].X + m_normals[j].Y * m_normals[k].Y);
				if (cosA > 0) // angle ==> 0 degrees
				{
					m_destPoly.Add(new IntPoint(Round(m_srcPoly[j].X + m_normals[k].X * m_delta),
					  Round(m_srcPoly[j].Y + m_normals[k].Y * m_delta)));
					return;
				}
				//else angle ==> 180 degrees   
			}
			else if (m_sinA > 1.0) m_sinA = 1.0;
			else if (m_sinA < -1.0) m_sinA = -1.0;

			if (m_sinA * m_delta < 0)
			{
				m_destPoly.Add(new IntPoint(Round(m_srcPoly[j].X + m_normals[k].X * m_delta),
				  Round(m_srcPoly[j].Y + m_normals[k].Y * m_delta)));
				m_destPoly.Add(m_srcPoly[j]);
				m_destPoly.Add(new IntPoint(Round(m_srcPoly[j].X + m_normals[j].X * m_delta),
				  Round(m_srcPoly[j].Y + m_normals[j].Y * m_delta)));
			}
			else
				switch (jointype)
				{
					case JoinType.jtMiter:
						{
							double r = 1 + (m_normals[j].X * m_normals[k].X +
							  m_normals[j].Y * m_normals[k].Y);
							if (r >= m_miterLim) DoMiter(j, k, r); else DoSquare(j, k);
							break;
						}
					case JoinType.jtSquare: DoSquare(j, k); break;
					case JoinType.jtRound: DoRound(j, k); break;
				}
			k = j;
		}
		//------------------------------------------------------------------------------

		internal void DoSquare(int j, int k)
		{
			double dx = Math.Tan(Math.Atan2(m_sinA,
				m_normals[k].X * m_normals[j].X + m_normals[k].Y * m_normals[j].Y) / 4);
			m_destPoly.Add(new IntPoint(
				Round(m_srcPoly[j].X + m_delta * (m_normals[k].X - m_normals[k].Y * dx)),
				Round(m_srcPoly[j].Y + m_delta * (m_normals[k].Y + m_normals[k].X * dx))));
			m_destPoly.Add(new IntPoint(
				Round(m_srcPoly[j].X + m_delta * (m_normals[j].X + m_normals[j].Y * dx)),
				Round(m_srcPoly[j].Y + m_delta * (m_normals[j].Y - m_normals[j].X * dx))));
		}
		//------------------------------------------------------------------------------

		internal void DoMiter(int j, int k, double r)
		{
			double q = m_delta / r;
			m_destPoly.Add(new IntPoint(Round(m_srcPoly[j].X + (m_normals[k].X + m_normals[j].X) * q),
				Round(m_srcPoly[j].Y + (m_normals[k].Y + m_normals[j].Y) * q)));
		}
		//------------------------------------------------------------------------------

		internal void DoRound(int j, int k)
		{
			double a = Math.Atan2(m_sinA,
			m_normals[k].X * m_normals[j].X + m_normals[k].Y * m_normals[j].Y);
			int steps = Math.Max((int)Round(m_StepsPerRad * Math.Abs(a)), 1);

			double X = m_normals[k].X, Y = m_normals[k].Y, X2;
			for (int i = 0; i < steps; ++i)
			{
				m_destPoly.Add(new IntPoint(
					Round(m_srcPoly[j].X + X * m_delta),
					Round(m_srcPoly[j].Y + Y * m_delta)));
				X2 = X;
				X = X * m_cos - m_sin * Y;
				Y = X2 * m_sin + Y * m_cos;
			}
			m_destPoly.Add(new IntPoint(
			Round(m_srcPoly[j].X + m_normals[j].X * m_delta),
			Round(m_srcPoly[j].Y + m_normals[j].Y * m_delta)));
		}
		//------------------------------------------------------------------------------
	}

	class ClipperException : Exception
	{
		public ClipperException(string description) : base(description) { }
	}
	//------------------------------------------------------------------------------

} //end ClipperLib namespace
